Published In
Computer Methods in Applied Mechanics and Engineering
Document Type
Post-Print
Publication Date
2010
Subjects
Discontinuous functions, Galerkin methods, Transport theory -- Mathematics, Finite element method
Abstract
Considering a simple model transport problem, we present a new finite element method. While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from standard DG and streamline diffusion methods, in that it uses a space of discontinuous trial functions tailored for stability. The new method, unlike the older approaches, yields optimal estimates for the primal variable in both the element size h and polynomial degree p, and outperforms the standard upwind DG method.
DOI
10.1016/j.cma.2010.01.003
Persistent Identifier
http://archives.pdx.edu/ds/psu/10685
Citation Details
Demkowicz, Leszek and Gopalakrishnan, Jay, "A Class of Discontinuous Petrov–Galerkin Methods. Part I: The Transport Equation" (2010). Mathematics and Statistics Faculty Publications and Presentations. 55.
http://archives.pdx.edu/ds/psu/10685
Description
NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics & Engineering. 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 Computer Methods in Applied Mechanics & Engineering April 2010, Vol. 199, Issue 23-24 p1558–1572.