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A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane. (English) Zbl 1174.65049

Summary: The finite element method (FEM) and the boundary element method (BEM) are combined to solve numerically an exterior quasilinear elliptic problem. Based on an appropriate transformation and the Fourier series expansion, the exact quasilinear artificial boundary conditions and a series of the corresponding approximations for the given problem are presented. Then, the original problem is reduced into an equivalent problem defined in a bounded computational domain. We provide error estimate for the Galerkin method. Numerical results are presented to illustrate the theoretical results.

MSC:

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