Symmetric coupling of boundary elements and Raviart–Thomas-type mixed finite elements in elastostatics

Summary.

Both mixed finite element methods and boundary integral methods are important tools in computational mechanics according to a good stress approximation. Recently, even low order mixed methods of Raviart–Thomas-type became available for problems in elasticity. Since either methods are robust for critical Poisson ratios, it appears natural to couple the two methods as proposed in this paper. The symmetric coupling changes the elliptic part of the bilinear form only. Hence the convergence analysis of mixed finite element methods is applicable to the coupled problem as well. Specifically, we couple boundary elements with a family of mixed elements analyzed by Stenberg. The locking-free implementation is performed via Lagrange multipliers, numerical examples are included.