All

What are you looking for?

All
Projects
Results
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286263" target="_blank" >RIV/00216208:11320/14:10286263 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1093/imanum/drt007" target="_blank" >http://dx.doi.org/10.1093/imanum/drt007</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1093/imanum/drt007" target="_blank" >10.1093/imanum/drt007</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems

  • Original language description

    This paper is concerned with the analysis of the discontinuous Galerkin (DG) finite element method applied to a nonstationary nonlinear convection-diffusion problem on quasi-uniform triangulations. Using the technique of Zhang & Shu (2004, SIAM J. Numer.Anal., 42, 641-666), we prove a priori error estimates which are uniform with respect to the diffusion coefficient epsilon -> 0 and valid even in the purely convective case. Zhang and Shu perform their analysis for various explicit schemes using an argument which relies heavily on mathematical induction. We extend the analysis to the method of lines using continuous mathematical induction and a nonlinear Gronwall-type lemma. For an implicit scheme, we prove that standard arguments cannot prove the desired estimates without additional assumptions. For this purpose, we use a suitable continuation of the discrete implicit solution and again use continuous mathematical induction to prove error estimates under a CFL-like condition. Finally,

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • 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

    2014

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    IMA Journal of Numerical Analysis

  • ISSN

    0272-4979

  • e-ISSN

  • Volume of the periodical

    34

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    42

  • Pages from-to

    820-861

  • UT code for WoS article

    000334676500017

  • EID of the result in the Scopus database