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Article
A Primal DPG Method Without a First-Order Reformulation
Computers & Mathematics with Applications
  • L. Demkowicz, University of Texas at Austin
  • Jay Gopalakrishnan, Portland State University
Document Type
Post-Print
Publication Date
10-1-2013
Subjects
  • Reformulation (Mathematical programming),
  • Poisson’s equation,
  • Mathematics -- Formulae,
  • Approximation theory
Disciplines
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.
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

DOI
10.1016/j.camwa.2013.06.029
Persistent Identifier
http://archives.pdx.edu/ds/psu/10585
Citation Information
Demkowicz, L. L., & Gopalakrishnan, J. J. (2013). A primal DPG method without a first-order reformulation. Computers & Mathematics With Applications, 66(6), 1058-1064.