Sponsor
This work was partially supported by the NSF under grant DMS-1211635 and by the AFOSR under grant FA9550-12-1-0484.
Published In
Computers & Mathematics with Applications
Document Type
Post-Print
Publication Date
10-2013
Subjects
Reformulation (Mathematical programming), Poisson’s equation, Mathematics -- Formulae, Approximation theory
Abstract
We show that it is possible to apply the DPG methodology without reformulating a second-order boundary value problem into a first-order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in addition to the primal interior variable.
Rights
Copyright © 2013 Elsevier Ltd. All rights reserved.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Locate the Document
DOI
10.1016/j.camwa.2013.06.029
Persistent Identifier
http://archives.pdx.edu/ds/psu/10585
Citation Details
Demkowicz, L. L., & Gopalakrishnan, J. J. (2013). A primal DPG method without a first-order reformulation. Computers & Mathematics With Applications, 66(6), 1058-1064.
Description
NOTICE: this is the author’s version of a work that was accepted for publication in Computers & Mathematics with Applications. 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. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, Volume 66, Issue 6, 2013
DOI: 10.1016/j.camwa.2013.06.029