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Numerical Algorithms
Published in: Numerical Algorithms 2/2020

18-04-2019 | Original Paper

A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems

Authors: Guanglong Ma, Martin Stynes

Published in: Numerical Algorithms | Issue 2/2020

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Abstract

The direct discontinuous Galerkin (DDG) finite element method, using piecewise polynomials of degree k ≥ 1 on a Shishkin mesh, is applied to convection-dominated singularly perturbed two-point boundary value problems. Consistency, stability and convergence of order k (up to a logarithmic factor) are proved in an energy-type norm appropriate to the method and problem. The results are robust, i.e., they hold uniformly for all values of the singular perturbation parameter. Numerical experiments confirm the theoretical convergence rate.
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Appendix
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Metadata
Title
A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems
Authors
Guanglong Ma
Martin Stynes
Publication date
18-04-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00701-1

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