This paper deals with a simple and straightforward procedure for automatic generation of finiteel... more This paper deals with a simple and straightforward procedure for automatic generation of finiteelement or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the boundary of a curved three-dimensional domain not so irregular can be expressed in spherical coordinates, with origin placed at a suitable location in its interior. An optimal numbering of mesh elements and nodes can be accomplished very easily. Several examples indicate that the generated meshes form a quasi-uniform family of partitions, as the corresponding value of the integer parameter increases, as long as the domain is not too distorted.
In recent papers (see e.g. , , and ) the author introduced a simple alternative of the n-simplex ... more In recent papers (see e.g. , , and ) the author introduced a simple alternative of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth curved domains. This technique is based upon trial-functions consisting of piecewise polynomials defined on straight-edged triangular or tetrahedral meshes, interpolating the Dirichlet boundary conditions at points of the true boundary. In contrast the test-functions are defined upon the standard degrees of freedom associated with the underlying method for polytopic domains. While method's mathematical analysis for two-dimensional domains was carried out in [25] and , this paper is devoted to the study of the three-dimensional case. Well-posedness, uniform stability and optimal a priori error estimates in the energy norm are demonstrated for a tetrahedron-based Lagrange family of finite elements. Unprecedented L 2 -error estimates for the class of problems considered in this work are also proved. A series of numerical examples illustrates the potential of the new technique. In particular its better accuracy at equivalent cost as compared to the isoparametric technique is highlighted. Moreover the great generality of the new approach is exemplified through a method with degrees of freedom other than nodal values.
This paper deals with a simple and straightforward procedure for automatic generation of finiteel... more This paper deals with a simple and straightforward procedure for automatic generation of finiteelement or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the boundary of a curved three-dimensional domain not so irregular can be expressed in spherical coordinates, with origin placed at a suitable location in its interior. An optimal numbering of mesh elements and nodes can be accomplished very easily. Several examples indicate that the generated meshes form a quasi-uniform family of partitions, as the corresponding value of the integer parameter increases, as long as the domain is not too distorted.
Considera-se neste artigo a indexacao automatica usando o processamento de documentos em linguage... more Considera-se neste artigo a indexacao automatica usando o processamento de documentos em linguagem natural, que e obtido com o auxilio de metodos linguisticos combinados com metodos estatisticos permitindo uma indexacao ponderada. A titulo ilustrativo descreve-set em linhas gerais, um sistema de indexacao desse genero denominado SPIRIT, o qual foi desenvolvido para o idioma frances por uma equipe de pesquisadores do CNRS. Enfim, sao tratados aspectos essenciais de sua adaptacao a lingua portuguesa. Descritores Ambiguidade. Analise sintetica. Entropia. Estatistica. Filtros. Indexacao automatica. Indexacao ponderada. Linguistica. Matrizes de precedencia. Metodo de aprendizado. Proximidade. Relacoes lexicosemânticas. Abstract This paper deals with automatic indexing based on linguistic and statistical methods, which aims to allow the processing of documents in natural language. The main lines of a system called SPIRIT, that uses such methods, and that was developed for the French Langu...
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020
One of the reasons for the success of the finite element method in Solid Mechanics, among other A... more One of the reasons for the success of the finite element method in Solid Mechanics, among other Applied Sciences, is its versatility to deal with bodies of arbitrary shape. In case the problem at hand is modeled by second‐order partial differential equations with Dirichlet conditions prescribed on a curvilinear boundary, method's isoparametric version for meshes consisting of curved triangles or tetrahedra has been mostly employed to recover the optimal approximation properties known to hold for polygonal or polyhedral domains and methods of order greater than one based on standard straight‐edged elements. However, besides algebraic and geometric inconveniences, the isoparametric technique is limited in scope, since its extension to degrees of freedom other than function values is not straightforward. In previous work the author introduced a simple alternative, which bypasses the above drawbacks without eroding qualitative approximation properties. Among other advantages, it can...
Advances in Applied Mathematics and Mechanics, 2010
Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have be... more Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have been increasingly exploited by several authors in the past ten years. It is generally claimed the alledged attractive geometrical flexibility of these methods, although they involve considerable increase of computational effort, as compared to continuous methods. This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic m-harmonic equations in a bounded domain of IR n , for n = 2 or n = 3, with m≥n + 1, as a valid and reasonable alternative to classical finite elements, or even to boundary element methods.
Computers & Mathematics with Applications, 2018
Among a few known techniques the isoparametric version of the finite element method for meshes co... more Among a few known techniques the isoparametric version of the finite element method for meshes consisting of curved triangles or tetrahedra is the one most widely employed to solve PDEs with essential conditions prescribed on curved boundaries. It allows to recover optimal approximation properties that hold for elements of order greater than one in the energy norm for polytopic domains. However, besides a geometric complexity, this technique requires the manipulation of rational functions and the use of numerical integration. We consider a simple alternative to deal with Dirichlet boundary conditions that bypasses these drawbacks, without eroding qualitative approximation properties. In the present work we first recall the main principle this technique is based upon, by taking as a model the solution of the Poisson equation with quadratic Lagrange finite elements. Then we show that it extends very naturally to viscous incompressible flow problems. Although the technique applies to any higher order velocity-pressure pairing, as an illustration a thorough study thereof is conducted in the framework of the Stokes system solved by the classical Taylor-Hood method.
The purpose of this work is two-fold: On the one hand it is aimed at presenting some arguments th... more The purpose of this work is two-fold: On the one hand it is aimed at presenting some arguments that justify the use of certain spaces of functions or vector fields in which the vorticity is to be searched for, in the framework of weak formulations of the incompressible Navier-Stokes equations expressed as a second order system in terms of this variable together with the velocity. On the other hand it is shown how the adopted formulations, when combined with a boundary condition uncoupling technique of the so-called Glowinski-Pironneau type, can be approximated bv finite element methods having similar convergence properties to those of methods previously proposed by the author (cf. ) $)$ to discretize the classical stream function-vorticity formulation of these equations. Throughout the work, an emphasis will be given to the case of the velocity- vorticity Stokes system, in which the main difficulties to overcome are encountered. More precisely, we mean the equivalence with the standard velocity-pressure formulation of the system of equations, and coupling boundary conditions.
Zeitschrift für angewandte Mathematik und Physik, 1998
This work introduces some uncoupling techniques for solving the three-dimensional incompressible ... more This work introduces some uncoupling techniques for solving the three-dimensional incompressible Navier-Stokes equations in the vorticity-velocity representation. Without any loss of essential aspects, the analysis is conducted for the case of the underlying Stokes system. For some of these uncoupled formulations, only scalar problems defined on the boundary of the flow domain need to be solved, in order to determine the key field in the methodology, that is, a suitable harmonic component of the vorticity.
In this work a unifying approach is presented that leads to bounds for the distance in natural no... more In this work a unifying approach is presented that leads to bounds for the distance in natural norms between solutions belonging to different spaces, of well-posed linear variational problems with the same input data. This is done in a general hilbertian framework, and in this sense, well-known inequalities such as Céa's or Babuška's for coercive and non coercive problems are extended and/or refined, as mere by-products of this unified setting. More particularly such an approach gives rise to both an improvement and a generalization to the weakly coercive case, of second Strang's inequality for abstract coercive problems. Additionally several aspects specific to linear variational problems are the subject of a thorough analysis beforehand, which also allows for clarifications and further refinements about the concept of weak coercivity.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2013
Um esquema de elementos finitos mistos de tipo mínimos quadrados é estudado para resolver as equa... more Um esquema de elementos finitos mistos de tipo mínimos quadrados é estudado para resolver as equac ¸ ões da convecc ¸ ão-difusão transientes expressas em func ¸ ão tanto do campo incógnito primário como do seu fluxo, incorporando ou não um termo reativo. Uma vez efetuada uma discretizac ¸ ão temporal à la Crank-Nicholson, o sistema de equac ¸ ões resultante permite uma aproximac ¸ ão estável desses 2 campos, com elementos finitos contínuos de Lagrange clássicos de grau arbitrário em geometria de tipo simplex ou não, em dimensão espacial qualquer. O esquema é convergente em espac ¸ o no sentido da média quadrática no que tange ao campo incógnito primário, a seu gradiente, à variável de fluxo e à divergência desta última, e no tempo num sentido apropriado para cada um desses campos. Os resultados numéricos atestam o bom desempenho do esquema, para quaisquer números de Péclet, confirmando as previsões teóricas, pelo menos no caso de camadas limite estreitas em que o método se mostra fracassado. A técnica é também comparada com outros métodos para resolver essas equac ¸ ões, incluindo 2 propostos recentemente pelo primeiro autor et al.
Two new Hermite finite elements are shown to be an advantageous alternative to wellknown mixed me... more Two new Hermite finite elements are shown to be an advantageous alternative to wellknown mixed methods in the simulation of diffusion processes in heterogeneous anisotropic media. Both are N-simplex based for N ¼ 2 and N ¼ 3 and provide flux continuity across inter-element boundaries. One of the methods denoted by P 2 H was introduced by the first author and collaborator for the case of homogeneous and isotropic media. Its extension to the case of heterogeneous and/or anisotropic cases is exploited here, keeping an implementation cost close to the popular Raviart-Thomas mixed finite element of the lowest order, known as RT 0 . The other method studied in detail in this work is a new Hermite version of the latter element denoted by RT 0 M. Formal results are given stating that, at least in the case of a constant diffusion, RT 0 M is significantly more accurate than RT 0 , although both elements have essentially the same implementation cost. A thorough comparative numerical study of the Hermite methods and RT 0 is carried out in the framework of highly heterogeneous media among other cases. It turns out that both are globally superior all the way, and roughly equivalent to each other in most cases.
Journal of Computational and Applied Mathematics, 2011
A mixed finite element scheme designed for solving the time-dependent advection-diffusion equatio... more A mixed finite element scheme designed for solving the time-dependent advection-diffusion equations expressed in terms of both the primal unknown and its flux, incorporating or not a reaction term, is studied. Once a time discretization of the Crank-Nicholson type is performed, the resulting system of equations allows for a stable approximation of both fields, by means of classical Lagrange continuous piecewise polynomial functions of arbitrary degree, in any space dimension. Convergence in the norm of H 1 × H(div) in space and in appropriate senses in time applying to this pair of fields is demonstrated.
Computers & Mathematics with Applications, 1979
A method for automatic generation of triangnlar finite element meshes for starshaped domains is i... more A method for automatic generation of triangnlar finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p. such that: minm>c T m(T) vp, p=l,Z,... p(T) and h(T) being respectively the dieter of the inscribed circle and the largest edge of a generated triangle T.
An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusi... more An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero.
Japan Journal of Industrial and Applied Mathematics, Feb 1, 2009
An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown tha... more An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown that convenient bounds for the time step value ensure L ∞ stability, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense are also demonstrated under certain conditions. Numerical results certify the good performance of the scheme.
This paper deals with a simple and straightforward procedure for automatic generation of finiteel... more This paper deals with a simple and straightforward procedure for automatic generation of finiteelement or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the boundary of a curved three-dimensional domain not so irregular can be expressed in spherical coordinates, with origin placed at a suitable location in its interior. An optimal numbering of mesh elements and nodes can be accomplished very easily. Several examples indicate that the generated meshes form a quasi-uniform family of partitions, as the corresponding value of the integer parameter increases, as long as the domain is not too distorted.
In recent papers (see e.g. , , and ) the author introduced a simple alternative of the n-simplex ... more In recent papers (see e.g. , , and ) the author introduced a simple alternative of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth curved domains. This technique is based upon trial-functions consisting of piecewise polynomials defined on straight-edged triangular or tetrahedral meshes, interpolating the Dirichlet boundary conditions at points of the true boundary. In contrast the test-functions are defined upon the standard degrees of freedom associated with the underlying method for polytopic domains. While method's mathematical analysis for two-dimensional domains was carried out in [25] and , this paper is devoted to the study of the three-dimensional case. Well-posedness, uniform stability and optimal a priori error estimates in the energy norm are demonstrated for a tetrahedron-based Lagrange family of finite elements. Unprecedented L 2 -error estimates for the class of problems considered in this work are also proved. A series of numerical examples illustrates the potential of the new technique. In particular its better accuracy at equivalent cost as compared to the isoparametric technique is highlighted. Moreover the great generality of the new approach is exemplified through a method with degrees of freedom other than nodal values.
This paper deals with a simple and straightforward procedure for automatic generation of finiteel... more This paper deals with a simple and straightforward procedure for automatic generation of finiteelement or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the boundary of a curved three-dimensional domain not so irregular can be expressed in spherical coordinates, with origin placed at a suitable location in its interior. An optimal numbering of mesh elements and nodes can be accomplished very easily. Several examples indicate that the generated meshes form a quasi-uniform family of partitions, as the corresponding value of the integer parameter increases, as long as the domain is not too distorted.
Considera-se neste artigo a indexacao automatica usando o processamento de documentos em linguage... more Considera-se neste artigo a indexacao automatica usando o processamento de documentos em linguagem natural, que e obtido com o auxilio de metodos linguisticos combinados com metodos estatisticos permitindo uma indexacao ponderada. A titulo ilustrativo descreve-set em linhas gerais, um sistema de indexacao desse genero denominado SPIRIT, o qual foi desenvolvido para o idioma frances por uma equipe de pesquisadores do CNRS. Enfim, sao tratados aspectos essenciais de sua adaptacao a lingua portuguesa. Descritores Ambiguidade. Analise sintetica. Entropia. Estatistica. Filtros. Indexacao automatica. Indexacao ponderada. Linguistica. Matrizes de precedencia. Metodo de aprendizado. Proximidade. Relacoes lexicosemânticas. Abstract This paper deals with automatic indexing based on linguistic and statistical methods, which aims to allow the processing of documents in natural language. The main lines of a system called SPIRIT, that uses such methods, and that was developed for the French Langu...
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020
One of the reasons for the success of the finite element method in Solid Mechanics, among other A... more One of the reasons for the success of the finite element method in Solid Mechanics, among other Applied Sciences, is its versatility to deal with bodies of arbitrary shape. In case the problem at hand is modeled by second‐order partial differential equations with Dirichlet conditions prescribed on a curvilinear boundary, method's isoparametric version for meshes consisting of curved triangles or tetrahedra has been mostly employed to recover the optimal approximation properties known to hold for polygonal or polyhedral domains and methods of order greater than one based on standard straight‐edged elements. However, besides algebraic and geometric inconveniences, the isoparametric technique is limited in scope, since its extension to degrees of freedom other than function values is not straightforward. In previous work the author introduced a simple alternative, which bypasses the above drawbacks without eroding qualitative approximation properties. Among other advantages, it can...
Advances in Applied Mathematics and Mechanics, 2010
Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have be... more Discontinuous Galerkin methods as a solution technique of second order elliptic problems, have been increasingly exploited by several authors in the past ten years. It is generally claimed the alledged attractive geometrical flexibility of these methods, although they involve considerable increase of computational effort, as compared to continuous methods. This work is aimed at proposing a combination of DGM and non-conforming finite element methods to solve elliptic m-harmonic equations in a bounded domain of IR n , for n = 2 or n = 3, with m≥n + 1, as a valid and reasonable alternative to classical finite elements, or even to boundary element methods.
Computers & Mathematics with Applications, 2018
Among a few known techniques the isoparametric version of the finite element method for meshes co... more Among a few known techniques the isoparametric version of the finite element method for meshes consisting of curved triangles or tetrahedra is the one most widely employed to solve PDEs with essential conditions prescribed on curved boundaries. It allows to recover optimal approximation properties that hold for elements of order greater than one in the energy norm for polytopic domains. However, besides a geometric complexity, this technique requires the manipulation of rational functions and the use of numerical integration. We consider a simple alternative to deal with Dirichlet boundary conditions that bypasses these drawbacks, without eroding qualitative approximation properties. In the present work we first recall the main principle this technique is based upon, by taking as a model the solution of the Poisson equation with quadratic Lagrange finite elements. Then we show that it extends very naturally to viscous incompressible flow problems. Although the technique applies to any higher order velocity-pressure pairing, as an illustration a thorough study thereof is conducted in the framework of the Stokes system solved by the classical Taylor-Hood method.
The purpose of this work is two-fold: On the one hand it is aimed at presenting some arguments th... more The purpose of this work is two-fold: On the one hand it is aimed at presenting some arguments that justify the use of certain spaces of functions or vector fields in which the vorticity is to be searched for, in the framework of weak formulations of the incompressible Navier-Stokes equations expressed as a second order system in terms of this variable together with the velocity. On the other hand it is shown how the adopted formulations, when combined with a boundary condition uncoupling technique of the so-called Glowinski-Pironneau type, can be approximated bv finite element methods having similar convergence properties to those of methods previously proposed by the author (cf. ) $)$ to discretize the classical stream function-vorticity formulation of these equations. Throughout the work, an emphasis will be given to the case of the velocity- vorticity Stokes system, in which the main difficulties to overcome are encountered. More precisely, we mean the equivalence with the standard velocity-pressure formulation of the system of equations, and coupling boundary conditions.
Zeitschrift für angewandte Mathematik und Physik, 1998
This work introduces some uncoupling techniques for solving the three-dimensional incompressible ... more This work introduces some uncoupling techniques for solving the three-dimensional incompressible Navier-Stokes equations in the vorticity-velocity representation. Without any loss of essential aspects, the analysis is conducted for the case of the underlying Stokes system. For some of these uncoupled formulations, only scalar problems defined on the boundary of the flow domain need to be solved, in order to determine the key field in the methodology, that is, a suitable harmonic component of the vorticity.
In this work a unifying approach is presented that leads to bounds for the distance in natural no... more In this work a unifying approach is presented that leads to bounds for the distance in natural norms between solutions belonging to different spaces, of well-posed linear variational problems with the same input data. This is done in a general hilbertian framework, and in this sense, well-known inequalities such as Céa's or Babuška's for coercive and non coercive problems are extended and/or refined, as mere by-products of this unified setting. More particularly such an approach gives rise to both an improvement and a generalization to the weakly coercive case, of second Strang's inequality for abstract coercive problems. Additionally several aspects specific to linear variational problems are the subject of a thorough analysis beforehand, which also allows for clarifications and further refinements about the concept of weak coercivity.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2013
Um esquema de elementos finitos mistos de tipo mínimos quadrados é estudado para resolver as equa... more Um esquema de elementos finitos mistos de tipo mínimos quadrados é estudado para resolver as equac ¸ ões da convecc ¸ ão-difusão transientes expressas em func ¸ ão tanto do campo incógnito primário como do seu fluxo, incorporando ou não um termo reativo. Uma vez efetuada uma discretizac ¸ ão temporal à la Crank-Nicholson, o sistema de equac ¸ ões resultante permite uma aproximac ¸ ão estável desses 2 campos, com elementos finitos contínuos de Lagrange clássicos de grau arbitrário em geometria de tipo simplex ou não, em dimensão espacial qualquer. O esquema é convergente em espac ¸ o no sentido da média quadrática no que tange ao campo incógnito primário, a seu gradiente, à variável de fluxo e à divergência desta última, e no tempo num sentido apropriado para cada um desses campos. Os resultados numéricos atestam o bom desempenho do esquema, para quaisquer números de Péclet, confirmando as previsões teóricas, pelo menos no caso de camadas limite estreitas em que o método se mostra fracassado. A técnica é também comparada com outros métodos para resolver essas equac ¸ ões, incluindo 2 propostos recentemente pelo primeiro autor et al.
Two new Hermite finite elements are shown to be an advantageous alternative to wellknown mixed me... more Two new Hermite finite elements are shown to be an advantageous alternative to wellknown mixed methods in the simulation of diffusion processes in heterogeneous anisotropic media. Both are N-simplex based for N ¼ 2 and N ¼ 3 and provide flux continuity across inter-element boundaries. One of the methods denoted by P 2 H was introduced by the first author and collaborator for the case of homogeneous and isotropic media. Its extension to the case of heterogeneous and/or anisotropic cases is exploited here, keeping an implementation cost close to the popular Raviart-Thomas mixed finite element of the lowest order, known as RT 0 . The other method studied in detail in this work is a new Hermite version of the latter element denoted by RT 0 M. Formal results are given stating that, at least in the case of a constant diffusion, RT 0 M is significantly more accurate than RT 0 , although both elements have essentially the same implementation cost. A thorough comparative numerical study of the Hermite methods and RT 0 is carried out in the framework of highly heterogeneous media among other cases. It turns out that both are globally superior all the way, and roughly equivalent to each other in most cases.
Journal of Computational and Applied Mathematics, 2011
A mixed finite element scheme designed for solving the time-dependent advection-diffusion equatio... more A mixed finite element scheme designed for solving the time-dependent advection-diffusion equations expressed in terms of both the primal unknown and its flux, incorporating or not a reaction term, is studied. Once a time discretization of the Crank-Nicholson type is performed, the resulting system of equations allows for a stable approximation of both fields, by means of classical Lagrange continuous piecewise polynomial functions of arbitrary degree, in any space dimension. Convergence in the norm of H 1 × H(div) in space and in appropriate senses in time applying to this pair of fields is demonstrated.
Computers & Mathematics with Applications, 1979
A method for automatic generation of triangnlar finite element meshes for starshaped domains is i... more A method for automatic generation of triangnlar finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p. such that: minm>c T m(T) vp, p=l,Z,... p(T) and h(T) being respectively the dieter of the inscribed circle and the largest edge of a generated triangle T.
An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusi... more An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero.
Japan Journal of Industrial and Applied Mathematics, Feb 1, 2009
An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown tha... more An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown that convenient bounds for the time step value ensure L ∞ stability, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense are also demonstrated under certain conditions. Numerical results certify the good performance of the scheme.
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