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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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • e-ISSN

  • 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