Error Analysis of Galerkin Methods for Dirichlet Problems Containing Boundary Singularities

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Abstract
This paper deals with a two-dimensional Poisson problem defined in a polygonal domain and having inhomogeneous Dirichlet boundary conditions. A Galerking method for obtaining approximations using triangular finite elements is described. The situation when the exact solution contains a singularity at a re-entrant corner of the boundary is considered, and for this an O(h) bound on the error in the Galerkin approximation is derived.

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