An algorithm for adaptive refinement of triangular element meshes

33rd Structures, Structural Dynamics and Materials Conference, 1992

A simple algoritlinl for adaptive and automatic h refinement of t,hree dimensional tetrahedral finite element meshes is presented. The algorithm is based on an aposteriori error indicator that is calculated by the finite element solver. The elrment subdivision algorithm is robust and rccilrsive. Smooth transition between large and small c~l(~lnents is achieved without significant degradation of the aspect rat,io of t,he elements in the n~e s h. An cxaniplr is presented to illustrate the utility of the approach.

Indian Journal of Engineering and Materials Sciences, 1999

Among the acce pt ab le numerical methods. Finite Element Analysis stands as the most acceptable one for problems characterised by partial differential equations. However. in accuracy in Finite Element An alysis is• unavoidable since a co ntinuum with infinite degrees of freedo m is modelled into finite degrees of freed o m. In addition to the mesh generation tas k being tedious and e rror prone. the accuracy and cost of the analysis de pe nd directly o n size. shape and number of d e ments in the mes h. The procedure of refining the mesh automatic ally based on the error estimate and distribution of the e rror is known as "adap ti ve" mesh refineme nt. A si mplified method called " Divide and Conquer" rule based on "Fuzzy Logic" is used to refi ne th e mes h by using Ir, p and Irp versions. Aut o matic mes h generato r develo ped in thi s paper based on Fuzzy log ic is able to develop well shaped elements. The program for automati c mes h gene ration and subsequent mesh re linement is developed in "C' language and the analys is is carried o ut usi ng " ANSYS " I package. Automatic mesh ge ne ratio n i~ app li cd to problems suc h as dam, square pl ate with a ho le. thi ck sphe rical press ure vessel and a co rbel and e rror less than 5 % is ac hi eved in most of th e cases.

Applied Sciences, 2021

The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.

Advances in Engineering Software, 2007

In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to reach a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper we propose the use of alternative mesh refinement with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria allow to obtain the maximum of accuracy for a prescribed cost. These adaptive strategies are based on a technique of error in constitutive relation (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas. This work proposes a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D.

IEEE Transactions on Magnetics, 1992

In this paper two strategies trying to reduce the overall number of flnite element computations needed in an adaptive meshing algorithm are proposed. In the flrst one numerical values of the estimated local error are used both to select the elemenb to be refined and to decide in how many new elements each of them will be Subdivided. In the second strategy a solution approximation and ita local error on a mesh are estimated from a previous approximate solution. For both methods the required algorithms are presented and the obtained results are compared and discussed.