Liu, Dongjie; Yu, Dehao A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane. (English) Zbl 1174.65049 J. Comput. Math. 26, No. 3, 378-389 (2008). 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. Cited in 3 Documents 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 Keywords:boundary element; coupling; finite element; exterior quasilinear elliptic problem; Fourier series expansion; quasilinear artificial boundary conditions; error estimate; Galerkin method; numerical results PDF BibTeX XML Cite \textit{D. Liu} and \textit{D. Yu}, J. Comput. Math. 26, No. 3, 378--389 (2008; Zbl 1174.65049) OpenURL