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An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472960" target="_blank" >RIV/00216208:11320/23:10472960 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=whj~QRTvzE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=whj~QRTvzE</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s10915-023-02153-1" target="_blank" >10.1007/s10915-023-02153-1</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

  • Original language description

    We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder Omega x (0, T). We employ the space-time discontinuous Galerkin method which enables us to use different meshes at different time levels in a natural way. The mesh adaptive algorithm is based on control of the interpolation error in the L-infinity(0, T; L-q(Omega))-norm. The goal is to construct a sequence of conforming triangular meshes in such a way that the interpolation error bound is under a given tolerance and the number of degrees of freedom is minimal. The resulting grids consist of anisotropic mesh elements with varying polynomial approximation degrees with respect to space. We present a theoretical framework of this approach as well as several numerical examples demonstrating the accuracy, efficiency, and applicability of the method.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • 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

    2023

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of Scientific Computing

  • ISSN

    0885-7474

  • e-ISSN

    1573-7691

  • Volume of the periodical

    95

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    31

  • Pages from-to

    36

  • UT code for WoS article

    000953450400004

  • EID of the result in the Scopus database

    2-s2.0-85150806238