We propose a three-field formulation for efficiently solving a twodimensional Stokes problem in t... more We propose a three-field formulation for efficiently solving a twodimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.
Actas Xvi Cedya Congreso De Ecuaciones Diferenciales Y Aplicaciones Vi Cma Congreso De Matematica Aplicada Las Palmas De Gran Canaria 21 24 Septiembre 1999 Vol 2 1999 Isbn 84 95286 18 1 Pags 1429 1436, 1999
We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipl... more We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 1 0 (Ω) derived by and complemented with the detailed work on polygonal domains developed by Grisvard [17]. We compute the action of the Lagrange multipliers using the natural H 1/2 00 scalar product, therefore no consistency error appears. As a byproduct, we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number shown by Mandel-Tezaur in . Numerical results that confirm our theoretical analysis are presented.
Based on the recent theoretical advances on the CDE (Bertozzi, 1991; Bertozzi and Constantin, 199... more Based on the recent theoretical advances on the CDE (Bertozzi, 1991; Bertozzi and Constantin, 1993) we introduce a numerical method for solving the CDE by means of a global cubic spline interpolation between nodes. This method is shown to be convergent for all time and numerically tested against exact solutions for the CDE, the well-known flows of the Kirchoff ellipses (Lamb,
Numerical Mathematics and Advanced Applications, 2008
We introduce a new domain decomposition method obtained when the classical iterative method of Uz... more We introduce a new domain decomposition method obtained when the classical iterative method of Uzawa is applied to the primal hybrid formulation for second order elliptic problems. In this formulation the Lagrange multipliers that inforce the continuity of the approximations across interfaces are expressed via the duality H −1/2 − H 1/2 , see for instance the works of Raviart-Thomas [5], Roberts-Thomas [6]. Usually, for numerical discretizations, this duality is worked out by means of some projection operator onto the L 2 space on the interfaces, see for instance work of Ben Belgacem . In our approach we use Riesz representation and replace the duality with the H 1/2 scalar product that is explicitly computed. As a consequence, we have a formulation in terms of a saddle point problem suitable for iterative techniques, see for instance, the recent survey by Bacuta [1].
We analyze here the bidimensional boundary value problems, for both Stokes and Navier-Stokes equa... more We analyze here the bidimensional boundary value problems, for both Stokes and Navier-Stokes equations, in the case where non standard boundary conditions are imposed. A well-posed vorticity-velocity-pressure formulation for the Stokes problem is introduced and its finite element discretization, which needs some stabilization, is then studied. We consider next the approximation of the Navier-Stokes equations, based on the previous approximation of the Stokes equations. For both problems, the convergence of the numerical approximation and optimal error estimates are obtained. Some numerical tests are also presented.
Fresh vegetables contaminated with Yersinia enterocolitica have been implicated in foodborne dise... more Fresh vegetables contaminated with Yersinia enterocolitica have been implicated in foodborne disease outbreaks. Surfaces of vegetables can become contaminated with pathogenic microorganisms through contact with soil, irrigation water, fertilizers, equipment, humans, and animals. One approach to reduce this contamination is to treat fresh produce with sanitizers. In this study, the ability of ozone to inactivate Y. enterocolitica inoculated in water and on potato surfaces was evaluated. Furthermore, the efficacy of ozone in reducing natural flora on whole potato was determined. Total aerobic mesophilic and psychrotrophic bacteria, total coliforms, and Listeria monocytogenes were enumerated. Finally, several disinfection kinetic models were considered to predict Y. enterocolitica inactivation with ozone. Treatments with ozone (1.4 and 1.9 ppm) for 1 min decreased the Y. enterocolitica population in water by 4.6 and 6.2 log CFU ml(-1), respectively. Furthermore, ozonated water (5 ppm) ...
Mathematical Methods in the Applied Sciences, 2002
We present a new variational formulation of Stokes problem of uid mechanics that allows to take i... more We present a new variational formulation of Stokes problem of uid mechanics that allows to take into account very general boundary conditions for velocity, tangential vorticity or pressure. This formulation conducts a well posed mathematical problem in a family of particular cases. Figure 2. Degrees of freedom on a triangular mesh.
ESAIM: Mathematical Modelling and Numerical Analysis, 2000
The hydrostatic approximation of the incompressible 3D stationary Navier Stokes équa- tions is wi... more The hydrostatic approximation of the incompressible 3D stationary Navier Stokes équa- tions is widely used m oceanography and other apphed sciences It appears through a limit process due to the anisotropy of the domam in use, an océan, and it is usually studied as such We consider m this paper an equivalent formulation to this hydrostatic approximation that mcludes Coriohs force and an additional pressure tetm that comes from takmg into account the pressure in the state équation for the density It therefore models a shght dependence of the density upon compression terms We study this model as an independent mathematical object and prove an existence theorem by means of a mixed variational formulation The proof uses a family of finite element spaces to discretize the prob- lem coupled with a limit piocess that yields the solution We finish this papei with an existence and umqueness resuit foi the evolutionaiy lmeai pioblem associated to this model This pioblem mcludes the same additional pressuie teim and Coriohs force
Computer Methods in Applied Mechanics and Engineering, 2008
We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipl... more We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 1 0 (Ω) derived by and complemented with the detailed work on polygonal domains developed by Grisvard [17]. We compute the action of the Lagrange multipliers using the natural H 1/2 00 scalar product, therefore no consistency error appears. As a byproduct, we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number shown by Mandel-Tezaur in . Numerical results that confirm our theoretical analysis are presented.
5. F. Dubois, M. Salaün, S. Salmon, Discrete harmonics for stream function vorticity Stokes pro... more 5. F. Dubois, M. Salaün, S. Salmon, Discrete harmonics for stream function vorticity Stokes problem, Technical report 325/99, IAT/CNAM, 1999 and article to appear. ... 6. V. Girault and P.-A. Raviart Finite Element Methods for the NavierStokes Equations. Theory and ...
This paper is devoted to the construction of fast solvers for penalty domain decomposition techni... more This paper is devoted to the construction of fast solvers for penalty domain decomposition techniques, based upon a posteriori error analysis. We introduce a penalty non-overlapping domain decomposition method (ddm) motivated by the a posteriori error analysis of the method proposed by Chacón and Chacón in [T. Chacón Rebollo, E. Chacón Vera, A non-overlapping domain decomposition method for the Stokes
We propose a three-field formulation for efficiently solving a twodimensional Stokes problem in t... more We propose a three-field formulation for efficiently solving a twodimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.
Actas Xvi Cedya Congreso De Ecuaciones Diferenciales Y Aplicaciones Vi Cma Congreso De Matematica Aplicada Las Palmas De Gran Canaria 21 24 Septiembre 1999 Vol 2 1999 Isbn 84 95286 18 1 Pags 1429 1436, 1999
We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipl... more We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 1 0 (Ω) derived by and complemented with the detailed work on polygonal domains developed by Grisvard [17]. We compute the action of the Lagrange multipliers using the natural H 1/2 00 scalar product, therefore no consistency error appears. As a byproduct, we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number shown by Mandel-Tezaur in . Numerical results that confirm our theoretical analysis are presented.
Based on the recent theoretical advances on the CDE (Bertozzi, 1991; Bertozzi and Constantin, 199... more Based on the recent theoretical advances on the CDE (Bertozzi, 1991; Bertozzi and Constantin, 1993) we introduce a numerical method for solving the CDE by means of a global cubic spline interpolation between nodes. This method is shown to be convergent for all time and numerically tested against exact solutions for the CDE, the well-known flows of the Kirchoff ellipses (Lamb,
Numerical Mathematics and Advanced Applications, 2008
We introduce a new domain decomposition method obtained when the classical iterative method of Uz... more We introduce a new domain decomposition method obtained when the classical iterative method of Uzawa is applied to the primal hybrid formulation for second order elliptic problems. In this formulation the Lagrange multipliers that inforce the continuity of the approximations across interfaces are expressed via the duality H −1/2 − H 1/2 , see for instance the works of Raviart-Thomas [5], Roberts-Thomas [6]. Usually, for numerical discretizations, this duality is worked out by means of some projection operator onto the L 2 space on the interfaces, see for instance work of Ben Belgacem . In our approach we use Riesz representation and replace the duality with the H 1/2 scalar product that is explicitly computed. As a consequence, we have a formulation in terms of a saddle point problem suitable for iterative techniques, see for instance, the recent survey by Bacuta [1].
We analyze here the bidimensional boundary value problems, for both Stokes and Navier-Stokes equa... more We analyze here the bidimensional boundary value problems, for both Stokes and Navier-Stokes equations, in the case where non standard boundary conditions are imposed. A well-posed vorticity-velocity-pressure formulation for the Stokes problem is introduced and its finite element discretization, which needs some stabilization, is then studied. We consider next the approximation of the Navier-Stokes equations, based on the previous approximation of the Stokes equations. For both problems, the convergence of the numerical approximation and optimal error estimates are obtained. Some numerical tests are also presented.
Fresh vegetables contaminated with Yersinia enterocolitica have been implicated in foodborne dise... more Fresh vegetables contaminated with Yersinia enterocolitica have been implicated in foodborne disease outbreaks. Surfaces of vegetables can become contaminated with pathogenic microorganisms through contact with soil, irrigation water, fertilizers, equipment, humans, and animals. One approach to reduce this contamination is to treat fresh produce with sanitizers. In this study, the ability of ozone to inactivate Y. enterocolitica inoculated in water and on potato surfaces was evaluated. Furthermore, the efficacy of ozone in reducing natural flora on whole potato was determined. Total aerobic mesophilic and psychrotrophic bacteria, total coliforms, and Listeria monocytogenes were enumerated. Finally, several disinfection kinetic models were considered to predict Y. enterocolitica inactivation with ozone. Treatments with ozone (1.4 and 1.9 ppm) for 1 min decreased the Y. enterocolitica population in water by 4.6 and 6.2 log CFU ml(-1), respectively. Furthermore, ozonated water (5 ppm) ...
Mathematical Methods in the Applied Sciences, 2002
We present a new variational formulation of Stokes problem of uid mechanics that allows to take i... more We present a new variational formulation of Stokes problem of uid mechanics that allows to take into account very general boundary conditions for velocity, tangential vorticity or pressure. This formulation conducts a well posed mathematical problem in a family of particular cases. Figure 2. Degrees of freedom on a triangular mesh.
ESAIM: Mathematical Modelling and Numerical Analysis, 2000
The hydrostatic approximation of the incompressible 3D stationary Navier Stokes équa- tions is wi... more The hydrostatic approximation of the incompressible 3D stationary Navier Stokes équa- tions is widely used m oceanography and other apphed sciences It appears through a limit process due to the anisotropy of the domam in use, an océan, and it is usually studied as such We consider m this paper an equivalent formulation to this hydrostatic approximation that mcludes Coriohs force and an additional pressure tetm that comes from takmg into account the pressure in the state équation for the density It therefore models a shght dependence of the density upon compression terms We study this model as an independent mathematical object and prove an existence theorem by means of a mixed variational formulation The proof uses a family of finite element spaces to discretize the prob- lem coupled with a limit piocess that yields the solution We finish this papei with an existence and umqueness resuit foi the evolutionaiy lmeai pioblem associated to this model This pioblem mcludes the same additional pressuie teim and Coriohs force
Computer Methods in Applied Mechanics and Engineering, 2008
We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipl... more We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 1 0 (Ω) derived by and complemented with the detailed work on polygonal domains developed by Grisvard [17]. We compute the action of the Lagrange multipliers using the natural H 1/2 00 scalar product, therefore no consistency error appears. As a byproduct, we obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number shown by Mandel-Tezaur in . Numerical results that confirm our theoretical analysis are presented.
5. F. Dubois, M. Salaün, S. Salmon, Discrete harmonics for stream function vorticity Stokes pro... more 5. F. Dubois, M. Salaün, S. Salmon, Discrete harmonics for stream function vorticity Stokes problem, Technical report 325/99, IAT/CNAM, 1999 and article to appear. ... 6. V. Girault and P.-A. Raviart Finite Element Methods for the NavierStokes Equations. Theory and ...
This paper is devoted to the construction of fast solvers for penalty domain decomposition techni... more This paper is devoted to the construction of fast solvers for penalty domain decomposition techniques, based upon a posteriori error analysis. We introduce a penalty non-overlapping domain decomposition method (ddm) motivated by the a posteriori error analysis of the method proposed by Chacón and Chacón in [T. Chacón Rebollo, E. Chacón Vera, A non-overlapping domain decomposition method for the Stokes
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