On a FEM--BEM formulation for an exterior quasilinear problem in the plane

Abstract

[Abstract] We use a version of the FEM--BEM method introduced by Costabel [ Boundary Elements IX, Vol. 1, C. A. Brebbia et al., eds., Springer-Verlag, 1987] and Han [ J. Comput. Math., 8 (1990), pp. 223--232] to discretize an exterior quasilinear problem. We provide error estimates for the Galerkin method and propose a fully discrete scheme based on simple quadrature formulas. Furthermore, we show that these numerical integration schemes preserve the optimal rates of convergence. Finally, we present results of numerical experiments involving our discretization method.