On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286263" target="_blank" >RIV/00216208:11320/14:10286263 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/imanum/drt007" target="_blank" >http://dx.doi.org/10.1093/imanum/drt007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imanum/drt007" target="_blank" >10.1093/imanum/drt007</a>
Alternative languages
Result language
angličtina
Original language name
On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems
Original language description
This paper is concerned with the analysis of the discontinuous Galerkin (DG) finite element method applied to a nonstationary nonlinear convection-diffusion problem on quasi-uniform triangulations. Using the technique of Zhang & Shu (2004, SIAM J. Numer.Anal., 42, 641-666), we prove a priori error estimates which are uniform with respect to the diffusion coefficient epsilon -> 0 and valid even in the purely convective case. Zhang and Shu perform their analysis for various explicit schemes using an argument which relies heavily on mathematical induction. We extend the analysis to the method of lines using continuous mathematical induction and a nonlinear Gronwall-type lemma. For an implicit scheme, we prove that standard arguments cannot prove the desired estimates without additional assumptions. For this purpose, we use a suitable continuation of the discrete implicit solution and again use continuous mathematical induction to prove error estimates under a CFL-like condition. Finally,
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GPP201%2F11%2FP414" target="_blank" >GPP201/11/P414: Higher order methods based on reconstruction for the solution of conservation laws</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IMA Journal of Numerical Analysis
ISSN
0272-4979
e-ISSN
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Volume of the periodical
34
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
42
Pages from-to
820-861
UT code for WoS article
000334676500017
EID of the result in the Scopus database
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