Developments and applications of the technique of the composite mesh

BERGALLO, M. B.; NEUMAN, C. E.; SONZOGNI, V. E.

Sao Paulo

Congreso; X World Congress on Computational Mechanics; 2012

USP

The technique of the Composite Mesh has been introduced in the 90’s, as it canbe seen in papers by the authors in the IV WCCM held in Buenos Aires. Since then somedevelopments and applications have been made in several kinds of problems.The technique -inspired in the mixtures theory of composite material- is based on theutilization of two finite element meshes of different element size sharing the whole domain.Each mesh is endowed with a participation factor. The composite mesh may be used for twodifferent aims. One of them is to provide a posteriori error estimates, and the other one is toreduce the discretization errors thus leading to improved numerical solutions.For the first case, it is shown that the residues at the connecting points of both meshesserve as a posteriori error estimates being able to detect the regions where mesh adaptationshould be conducted. This aspect has been tested in different kind of problems and comparedwith other error estimates.The composite mesh may be used also to provide an improved numerical solution. Thisis performed by a suitable choice of the participation factors. Important reduction in the dis-cretization errors has been obtained for a wide class of problems, including those with bordersingularities. This improved solutions are obtained without increasing the computational costas the problem size to be solved is of the same order of that for the fine element mesh.Applications have been made to elliptic and parabolic problems in regular domains orin the presence of border singularities. Problems from structural mechanics (elastic analysisof plain stress and plates), as well as catalytic chemical reactors have also been addressed.It can be mentioned that the technique of the composite mesh has been also appliedin the frame of multigrid solving, showing interesting reductions in the solution errors, andmaking use of the fact that mesh with different size are available in the process.In this paper we make a review of the advances in this technique and present someresults on different application areas. We include some results both on error estimation andon solution improvement