Finite Element Method for the Solution of a Potential Theory Integral Equation

摘要

A finite element approximation for an integral equation of the second kind deduced from a potential theory boundary-value problem in two variables is discussed. The equation is shown to admit a unique solution, to be variational and coercive in the Hilbert space of functions sigma an element of H/sup 1/2/(GAMMA), integral/sub GAMMA/sigma d gamma = 0. The Galerkin method with finite elements as trial functions is shown to lead to an optimal rate of convergence. (ERA citation 04:055773)