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Article
The DPG-Star Method
Portland Institute for Computational Science Publications
  • Leszek Demkowicz, University of Texas at Austin
  • Jay Gopalakrishnan, Portland State University
  • Brendan Keith, University of Texas at Austin
Document Type
Pre-Print
Publication Date
11-1-2018
Subjects
  • Finite element method,
  • Inequalities (Mathematics),
  • Discontinuous functions,
  • Galerkin methods,
  • Numerical analysis
Disciplines
Abstract

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly garnered perspective. Notably, DPG* and DPG methods can be seen as generalizations of LL* and least-squares methods, respectively. A priori error analysis and a posteriori error control for the DPG* method are considered in detail. Reports of several numerical experiments are provided which demonstrate the essential features of the new method. A notable difference between the results from the DPG* and DPG analyses is that the convergence rates of the former are limited by the regularity of an extraneous Lagrange multiplier variable.

Description

This is the pre-print version of the article.

Persistent Identifier
https://archives.pdx.edu/ds/psu/26575
Citation Information
Leszek Demkowicz, Jay Gopalakrishnan and Brendan Keith. "The DPG-Star Method" (2018)
Available at: http://works.bepress.com/jay-gopalakrishnan/108/