On epsilon-uniform error estimates for singularly perturbed problems in the DG method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10129887" target="_blank" >RIV/00216208:11320/13:10129887 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_40" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-642-33134-3_40</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-33134-3_40" target="_blank" >10.1007/978-3-642-33134-3_40</a>
Alternative languages
Result language
angličtina
Original language name
On epsilon-uniform error estimates for singularly perturbed problems in the DG method
Original language description
In this paper we present the analysis of the discontinuous Galerkin (DG) finite element method applied to a nonstationary nonlinear convection-diffusion problem. Using the technique of Zhang and Shu (2004), originally for explicit schemes, we prove apriori error estimates uniform with respect to the diffusion coefficient and valid even in the purely convective case. We extend the cited analysis to the method of lines using continuous mathematical induction and a nonlinear Gronwall-type lemma. For an implicit scheme, we prove that there does not exist a Gronwall-type lemma capable of proving the desired estimates using standard arguments. Next, we use a suitable continuation of the implicit solution and use continuous mathematical induction to prove error estimates under a CFL-like condition.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Numerical Mathematics and Advanced Applications 2011
ISBN
978-3-642-33133-6
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
369-378
Publisher name
Springer-Verlag
Place of publication
Berlin, Heidelberg
Event location
Leicester, United Kingdom
Event date
Sep 5, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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