Adaptive H- and H- R methods for Symm's integral equation

Abstract

In this paper we present the adaptive h-, r- and h- r methods for the Gàlerkin approximation of Symm's integral equation. The a posteriori error estimate depends on a localized a priori error estimate and local finite differences of the computed solution. The optimal mesh for these three methods is obtained by using a mesh grading function. The numerical results for a polygonal problem, and a comparison between our error estimate and the residual error estimate, are also presented. Moreover, we briefly describe how to apply our method to a two-dimensional elasticity problem.