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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptivní metody pro numerické řešení parciálních diferenciálních rovnic: analýza, odhady chyb a iterativní řešiče</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Advances in Computational Mathematics

ISSN

1019-7168

e-ISSN

1572-9044

Svazek periodika

48

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

54

Kód UT WoS článku

000839636700001

EID výsledku v databázi Scopus

2-s2.0-85147148016