Mortar Boundary Elements
Provides a theoretical foundation for non-conforming domain decompositions in boundary element methods, but the contribution is incremental as it extends existing mortar techniques to a specific class of equations.
The paper develops a mortar boundary element method for 3D hypersingular integral equations, proving almost quasi-optimal convergence in broken Sobolev norms. Numerical results validate the theory.
We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. Numerical results confirm the theory.