Sponsor
Demkowicz was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615], and by a research contract with Boeing. Gopalakrishnan was supported in part by the National Science Foundation under grant DMS-0713833. Niemi was supported in part by KAUST.
Published In
Applied Numerical Mathematics
Document Type
Post-Print
Publication Date
2012
Subjects
Discontinuous functions, Numerical analysis, Diffusion processes, Matrices -- Norms, Reaction-diffusion equations
Abstract
We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only.
Rights
Copyright 2012 Published by Elsevier B.V.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Locate the Document
DOI
10.1016/j.apnum.2011.09.002
Persistent Identifier
http://archives.pdx.edu/ds/psu/10613
Citation Details
Published as: Demkowicz, L., Gopalakrishnan, J., & Niemi, A. H. (2012). A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Applied numerical mathematics, 62(4), 396-427.
Description
NOTICE: this is the author’s version of a work that was accepted for publication in Applied Numerical Mathematics. 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 Applied Numerical Mathematics, Vol. 62 Issue 4, 2012.