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On a FEM-BEM formulation for an exterior quasilinear problem in the plane. (English) Zbl 0986.65113
The authors use a version of the so-called symmetric FEM-BEM method introduced independently by {\it M. Costabel} [Boundary Elements IX, Vol. 1, A. Brebbia et al., eds., Springer-Verlag, Berlin (1987; Zbl 0632.73077)] and {\it H. Han} [J. Comput. Math. 8, No. 3, 223-232 (1990; Zbl 0712.65093)] to discretize an exterior quasilinear problem. (The FEM-BEM method is a coupling of the finite element method (FEM) and the boundary element method (BEM).) The authors provide error estimates for the Galerkin method and propose a fully discrete scheme based on simple quadrature formulas. They show that these numerical integration schemes preserve the optimal rate of convergence. Finally, they present results of numerical experiments involving their discretization method.

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
35J65Nonlinear boundary value problems for linear elliptic equations
65N38Boundary element methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
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