Coupling of Mixed Finite Elements and Boundary Elements for A Hyperelastic Interface Problem

Abstract

We apply the coupling of mixed finite elements and boundary integral methods, using two integral equations on the coupling boundary, to study the weak solvability of a nonlinear elliptic problem arising in elastostatics. Our procedure is based on both the usual Brezzi's theory for linear constrained variational problems and some fundamental tools from nonlinear functional analysis. We derive existence and uniqueness of solution for the continuous variational formulations and provide general approximation results for the corresponding Galerkin schemes. Although we consider bounded domains, the same analysis applies for the case in which the boundary element region is unbounded.