A Finite Element-Capacitance Matrix Method for the Elliptic Problem

Abstract

The capacitance matrix method for finite element approximation of the symmetric elliptic problem with the Dirichlet condition on an arbitrary region is considered. Two variants of this method are presented, which correspond to the situations when the single and double layer potential are used. It is shown that the condition number of the capacitance matrix C is $O(h^{ - 1} )$ for the first variant and the eigenvalues of C are positive and independent of h for the second variant where h is the mesh-size of the triangulation.