Exponential Scaling and the Time Growth of the Error of DG for Advection-Reaction Problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10407768" target="_blank" >RIV/00216208:11320/19:10407768 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/chapter/10.1007/978-3-319-96415-7_91" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-319-96415-7_91</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-96415-7_91" target="_blank" >10.1007/978-3-319-96415-7_91</a>

Result language
angličtina
Original language name
Exponential Scaling and the Time Growth of the Error of DG for Advection-Reaction Problems
Original language description
We present an overview of the results of the authors' paper (Kučera and Shu, IMA J Numer Anal, to appear) on the time growth of the error of the discontinuous Galerkin (DG) method and set them in appropriate context. The application of Gronwall's lemma gives estimates which grow exponentially in time even for problems where such behavior does not occur. In the case of a nonstationary advection-diffusion equation we can circumvent this problem by considering a general space-time exponential scaling argument. Thus we obtain error estimates for DG which grow exponentially not in time, but in the time particles carried by the flow field spend in the spatial domain. If this is uniformly bounded, one obtains an error estimate of the form C(h^(p+1/2)), where C is independent of time.We discuss the time growth of the exact solution and the exponential scaling argument and give an overview of results from Kučera and Shu (IMA J Numer Anal, to appear) and the tools necessary for the analysis.
Czech name
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Czech description
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Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Numerical Mathematics and Advanced Applications ENUMATH 2017
ISBN
978-3-319-96414-0
ISSN
1439-7358
e-ISSN
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Number of pages
9
Pages from-to
963-971
Publisher name
Springer
Place of publication
Cham
Event location
Voss, Norway
Event date
Sep 25, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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