Analysis and Numerical Realization of Coupled BEM and FEM for Nonlinear Exterior Problems

The paper presents main results of the investigation of the coupled BEM and FEM applied to a nonlinear generally nonmonotone exterior boundary value problem. The problem consists of a nonlinear differential equation considered in an annular bounded domain and the Laplace equation outside. These equations are equipped with boundary and transmission conditions. The problem is reformulated in a weak sense and combined with an integral equation. The discretization is carried out by the coupled finite element -- boundary element method. The attention is paid to the existence of the solution, the convergence of the method and the solution of the coupled discrete problem. The method is applied to compressible inviscid flow past an airfoil and the solution of the discrete problem is treated. 1 Formulation of the Problem Let\Omega \Gamma ae IR 2 be a bounded domain with a Lipschitz continuous boundary @\Omega \Gamma = \Gamma 0 [\Gamma. Here, \Gamma 0 ; \Gamma are simple closed curves, \..