Sponsor
This work was partly supported by AFOSR grant FA9550-17-1-0090. Numerical studies were facilitated by the Portland Institute of Sciences (PICS) established under NSF grant DMS-1624776. Paulina Sepúlveda has received funding from the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU) and BCAM “Severo Ochoa” accreditation of excellence SEV-2013-0323 and SEV-2017-0718.
Document Type
Post-Print
Publication Date
10-2018
Subjects
Numerical analysis, Discontinuous functions, Galerkin methods
Abstract
A spacetime 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 wellposedness 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 spacetime domain. The potential for using the built-in error estimator of the DPG method for an adaptivity mesh refinement strategy in two and three dimensions is also presented.
Persistent Identifier
https://archives.pdx.edu/ds/psu/26576
Citation Details
Gopalakrishnan, Jay and Sepulveda, Paulina, "A Spacetime DPG Method for the Wave Equation in Multiple Dimensions" (2018). Portland Institute for Computational Science Publications. 14.
https://archives.pdx.edu/ds/psu/26576
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document.