Study of FEM Errors for Elliptic 2D Problems with Border Singularities

Abstract

In recent years composite mesh methods aiming to construct numerical models where two or more finite element meshes of different granularities are superimposed over the whole domain of the problem were studied by the authors. The focus
is stressed 011 elliptic problems where the domains present border singularities in order to assess the different kinds of error estimations mixed mesh, Zienkiewicz-Zhu, Zadunaisky's- and their relationships. Estimation of residues and errors for some examples in planar domains is perfomed. Three main illustrating examples are treated here: (1) test problems based 011 variants of the Poisson equation with
boundary conditions of Dirichlet, Neuman and Robin type, (2) elliptic (stationary) advection-diffusion equation with boundary conditions of Dirichlet, Neuman and Robin type; and (3) elliptic problems arising from linear elasticity in plane stress.