On the Time Growth of the Error of the Discontinuous Galerkin Method for Advection-reaction Problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422671" target="_blank" >RIV/00216208:11320/20:10422671 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1578/830" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1578/830</a>
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
On the Time Growth of the Error of the Discontinuous Galerkin Method for Advection-reaction Problems
Original language description
This contribution presents an overview of the results of the paper Kučera & Shu (2019) on the time growth of the error of the discontinuous Galerkin (DG) method. When estimating quantities of interest in differential equations, the application of Gronwall's lemma gives estimates which grow exponentially in time even for problems where such behavior is unnatural. In the case of a non-stationary 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 p is the degree of polynomials used in the DG method and 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 & Shu (2019) and the tools necessary for the analysis.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the Conference Algoritmy 2020
ISBN
978-80-227-5032-5
ISSN
—
e-ISSN
—
Number of pages
8
Pages from-to
221-228
Publisher name
Vydavateľstvo SPEKTRUM
Place of publication
Bratislava
Event location
Vysoké Tatry - Podbanské
Event date
Sep 10, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—