Coupling of HDG with a double-layer potential BEM
Provides a theoretically sound and optimally convergent coupling method for transmission problems, but is incremental as it extends existing HDG-BEM coupling techniques.
The paper proposes a new coupling of HDG with double-layer potential BEM for transmission problems, proving optimal convergence and superconvergence estimates supported by numerical experiments.
In this paper we propose and analyze a new coupling procedure for the Hybridizable Discontinuous Galerkin Method with Galerkin Boundary Element Methods based on a double layer potential representation of the exterior component of the solution of a transmission problem. We show a discrete uniform coercivity estimate for the non-symmetric bilinear form and prove optimal convergence estimates for all the variables, as well as superconvergence for some of the discrete fields. Some numerical experiments support the theoretical findings.