A space-time DPG method for the wave equation in multiple dimensions

Abstract

A space-time discontinuous Petrov–Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The well-posedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in detail for a simple domain in arbitrary dimensions. The DPG method based on the weak formulation is then studied theoretically and numerically. Error estimates and numerical results are presented for triangular, rectangular, tetrahedral, and hexahedral meshes of the space-time domain. The potential for using the built-in error estimator of the DPG method for an adaptive mesh refinement strategy in two and three dimensions is also presentedThis work was partly supported by AFOSR grant FA9550–17–1–0090. Numerical studies were partially facilitated by the Portland Institute of Sciences (PICS) established under NSF grant DMS–1624776