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Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. (English) Zbl 1276.65066
The paper deals with the symmetric coupling of the finite element method and the boundary element method for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. The authors introduce some $$(h-h/2)$$ - type error estimators for the coupling of FEM and BEM and apply a symmetric coupling method and the lowest-order Galerkin scheme to obtain a (nonlinear) system of coupled FEM-BEM equations.

##### MSC:
 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J60 Nonlinear elliptic equations
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