Abstract
This paper presents a brief survey on the investigation of the coupled BEM and FEM applied to a nonlinear exterior boundary value problem. The aim is to find the solution of a nonlinear partial differential equation considered in an annular bounded domain and the Laplace equation outside. These equations are bound together by transmission conditions and are equipped with boundary conditions. The nonlinear problem in the interior domain is combined with an integral equation obtained with the aid of potential theory and then the whole problem is reformulated in a weak sense. The discretization is carried out by the coupled finite element — boundary element method. We discuss the existence and uniqueness of the solution of the discrete as well continuous problem, the convergence of approximate solutions to an exact one, provided the size of the grid tends to zero, and the iterative solution of the nonlinear discrete problem. Proofs are the subject of more detailed papers (see, e.g., [5]).
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