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Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452950" target="_blank" >RIV/00216208:11320/22:10452950 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=v3ZKdCONje" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=v3ZKdCONje</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s10444-022-09968-w" target="_blank" >10.1007/s10444-022-09968-w</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes

  • Original language description

    This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated polygonal/polyhedral meshes are employed for the coarse mesh approximation. We recall that within the two-grid setting, while it is necessary to solve a nonlinear problem on the coarse approximation space, only a linear problem must be computed on the original fine finite element space. In this article, the coarse space will be constructed by agglomerating elements from the original fine mesh. Here, we extend the existing a priori and a posteriori error analysis for the two-grid hp-version discontinuous Galerkin finite element method from Congreve et al. [1] for coarse meshes consisting of standard element shapes to include arbitrarily agglomerated coarse grids. Moreover, we develop an hp-adaptive two-grid algorithm to adaptively design the fine and coarse finite element spaces; we stress that this is undertaken in a fully automatic manner, and hence can be viewed as blackbox solver. Numerical experiments are presented for two- and three-dimensional problems to demonstrate the computational performance of the proposed hp-adaptive two-grid 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

    2022

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Advances in Computational Mathematics

  • ISSN

    1019-7168

  • e-ISSN

    1572-9044

  • Volume of the periodical

    48

  • Issue of the periodical within the volume

    5

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    31

  • Pages from-to

    54

  • UT code for WoS article

    000839636700001

  • EID of the result in the Scopus database

    2-s2.0-85147148016