Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems

TL;DR

This paper analyzes the stability and well-posedness of symmetric and non-symmetric FEM-BEM coupling methods, including Johnson-Nédélec coupling, for nonlinear elasticity problems without restrictive mesh or boundary assumptions.

Contribution

It proves the well-posedness and uniqueness of Galerkin solutions for these couplings using standard discretizations, without relying on interior boundaries or mesh-size assumptions.

Findings

Coupling formulations are well-posed and admit unique solutions.

Analysis does not depend on interior Dirichlet boundaries.

No restrictions on mesh-size for discretizations.

Abstract

We consider symmetric as well as non-symmetric coupling formulations of FEM and BEM in the frame of nonlinear elasticity problems. In particular, the Johnson-N\'ed\'elec coupling is analyzed. We prove that these coupling formulations are well-posed and allow for unique Galerkin solutions if standard discretizations by piecewise polynomials are employed. Unlike prior works, our analysis does neither rely on an interior Dirichlet boundary to tackle the rigid body motions nor on any assumption on the mesh-size of the discretization used.