Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation

We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h$$\end{document}- and p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces.