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Article
A Class of Discontinuous Petrov–Galerkin Methods. II. Optimal Test Functions
Numerical Methods for Partial Differential Equations
  • Leszek Demkowicz, University of Texas at Austin
  • Jay Gopalakrishnan, Portland State University
Document Type
Pre-Print
Publication Date
1-1-2010
Subjects
  • Galerkin methods,
  • Diffusion processes,
  • Reaction-diffusion equations
Abstract
We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes having test function spaces that are automatically computable to guarantee stability. Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well posedness of the undiscretized problem. Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework wherein test functions, arbitrarily close to the optimal ones, can be locally computed. The idea is presented abstractly and its feasibility illustrated through several theoretical and numerical examples.
Description

This is the pre-peer reviewed version of the following article: Demkowicz, L., & Gopalakrishnan, J.(2011). A Class of Discontinuous Petrov–Galerkin Methods. II. Optimal Test Functions. Numerical Methods for Partial Differential Equations, Vol. 27, Issue 1, pp. 70-105, which has been published in final form at: http://dx.doi.org/10.1002/num.20640

DOI
10.1002/num.20640
Persistent Identifier
http://archives.pdx.edu/ds/psu/10653
Citation Information
Leszek Demkowicz and Jay Gopalakrishnan. "A Class of Discontinuous Petrov–Galerkin Methods. II. Optimal Test Functions" Numerical Methods for Partial Differential Equations (2010)
Available at: http://works.bepress.com/jay-gopalakrishnan/6/