hp non-conforming a priori error analysis of an Interior Penalty Discontinuous Galerkin BEM for the Helmholtz equation

This work is concerned with the construction and the hp non-conforming a priori error analysis of a Discontinuous Galerkin DG numerical scheme applied to the hypersingular integral equation related to the Helmholtz problem in 3D. The main results of this article are an error bound in a norm suited to the problem and in the L-2-norm. Those bounds are quasi-optimal for the h-convergence and the p-convergence. Various formulation choices and penalty functions are theoretically discussed. In particular we show that a penalty function of the shape h(2)/p Some numerical experiments confirm the expected rates of convergence and the effect of the penalty function. leads to a quasi-optimal convergence of the scheme. (C) 2020 Elsevier Ltd. All rights reserved.