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Zbl 1174.65049
Liu, Dongjie; Yu, Dehao
A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane. (English)
[J] J. Comput. Math. 26, No. 3, 378-389 (2008). ISSN 0254-9409; ISSN 1991-7139/e

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 2000:: *65N30 Finite numerical methods (BVP of PDE)
65N38 Boundary element methods (BVP of PDE)
35J65 (Nonlinear) BVP for (non)linear elliptic equations
65N15 Error bounds (BVP of PDE)

Keywords: boundary element; coupling; finite element; exterior quasilinear elliptic problem; Fourier series expansion; quasilinear artificial boundary conditions; error estimate; Galerkin method; numerical results

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Zentralblatt MATH Berlin [Germany]