The boundary element numerical method for two-dimensional linear quadratic elliptic problems. I. Neumann control

Abstract

For two-dimensional distributed control systems governed by the Laplace equation, the boundary element method is an efficient numerical method to solve problems whose quadratic cost involves boundary integrals only. In this paper we formulate a duality-boundary integral equation scheme and use piecewise constant boundary elements to approximate the problem. This method involves discretization of the boundary curve only and it can conveniently handle the compatibility constraint due to the Neumann data. Convergence and optimal error estimates O ( h ) \mathcal {O}(h) have been proved. Numerical data for the case of a disk are computed to illustrate the theory.