Estimación De Error A Posteriori Para Problemas Elípticos Con Singularidades En El Borde

Abstract

Composite mesh methods that deal with the construction of numerical models where two
or more finite element meshes of different granularities are superimposed over de whole
domains of the problem where studied by the authors in the past five years. The focus
of this work is stressed on elliptic problems where border singularities, and the associated
lowering of order, are present.
Estimation of residues and errors for some examples are treated in this paper: (1)
the test problems based on variants of the Laplace equation in domains where the geometry
leads to the lowering of the order; (2) the elliptic stationary equations derived from
advection-diffusion problem with boundary conditions of Robin type, where in these cases
the singularities are associated with the boundary conditions.
The second set of examples are associated to problems drawn from Chemical Engineering
with the aim of providing reasonable a posteriori error estimates.
Our numerical model is composed by different finite element meshes and the properties
of the problem are obtained by adding those of the component meshes multiplied by a
participation factor