Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains

Abstract

In the two first parts of this work [RAIRO Model. Math. Anal. Numer., 24 (1990), pp. 27e52], [RAIRO Model. Math. Anal. Numer., 24 (1990), pp. 343–367] formulas giving the coefficients arising in the singular expansion of the solutions of elliptic boundary value problems on nonsmooth domains are investigated. Now, for the case of homogeneous strongly elliptic operators with constant coefficients on polygonal domains, the solution of such problems by the finite element method is considered. In order to approximate the solution or the coefficients, different methods are used based on the expressions of the coefficients that were obtained in the first two parts; the dual singular function method is also generalized.