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

Liu, Dongjie; Yu, Dehao

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.

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