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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 &amp; 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&apos;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 &amp; 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