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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 M. Costabel [Boundary Elements IX, Vol. 1, A. Brebbia et al., eds., Springer-Verlag, Berlin (1987; Zbl 0632.73077)] and 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.
Reviewer: M.Lenard (Kuwait)

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
65N38 Boundary element methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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