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Zbl 0986.65113
Meddahi, Salim; González, María; Pérez, Pablo
On a FEM-BEM formulation for an exterior quasilinear problem in the plane. (English)
[J] SIAM J. Numer. Anal. 37, No.6, 1820-1837 (2000). ISSN 0036-1429; ISSN 1095-7170/e

The authors use a version of the so-called symmetric FEM-BEM method introduced independently by {\it M. Costabel} [Boundary Elements IX, Vol. 1, A. Brebbia et al., eds., Springer-Verlag, Berlin (1987; Zbl 0632.73077)] and {\it 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.
[M.Lenard (Kuwait)]

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35J65 (Nonlinear) BVP for (non)linear elliptic equations
65N38 Boundary element methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)

Keywords: exterior quasilinear problem; coupling; finite element method; boundary element method; error estimates; Galerkin method; convergence; numerical experiments

Citations: Zbl 0632.73077; Zbl 0712.73077; Zbl 0712.65093

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