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.

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.

DOI

10.1016/j.apnum.2011.09.002

Persistent Identifier

http://archives.pdx.edu/ds/psu/10613

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