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A solution method for a certain nonlinear interface problem in unbounded domains. (English) Zbl 1109.65309
Summary: In this paper, we consider a kind of nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element and boundary element by adding an auxiliary circle. We first derive the optimal error estimate of finite element approximation to the coupled FEM-BEM problem. Then we introduce a preconditioning steepest descent method for solving the discrete system by constructing a cheap domain decomposition preconditioner. Moreover, we give a complete analysis to the convergence speed of this iterative method.

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
65R20 Numerical methods for integral equations
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