On the uniform stability of the space-time discontinuous Galerkin method for nonstationary problems in time-dependent domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331415" target="_blank" >RIV/00216208:11320/16:10331415 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/issue/view/19" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/issue/view/19</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the uniform stability of the space-time discontinuous Galerkin method for nonstationary problems in time-dependent domains

Popis výsledku v původním jazyce

In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convection-diusion-reaction problem in time-dependent domains formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The stability is uniform with respect to the diusion coecient. The ALE method replaces the classical partial time derivative with the so called ALE-derivative and an additional convective term. In the second part of the paper we discretize our problem using the space-time discontinuous Galerkin method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The space discretization uses piecewise polynomial approximations of degree p greater than 1, in time we use only piecewise linear discretization. Finally in the third part of the paper we present our results concerning the uniform unconditional stability of the method.

Název v anglickém jazyce

On the uniform stability of the space-time discontinuous Galerkin method for nonstationary problems in time-dependent domains

Popis výsledku anglicky

In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convection-diusion-reaction problem in time-dependent domains formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The stability is uniform with respect to the diusion coecient. The ALE method replaces the classical partial time derivative with the so called ALE-derivative and an additional convective term. In the second part of the paper we discretize our problem using the space-time discontinuous Galerkin method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The space discretization uses piecewise polynomial approximations of degree p greater than 1, in time we use only piecewise linear discretization. Finally in the third part of the paper we present our results concerning the uniform unconditional stability of the method.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-00522S" target="_blank" >GA13-00522S: Kvalitativní analýza a numerické řešení problémů proudění v obecně časově závislých oblastech s různými okrajovými podmínkami</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

PROCEEDINGS OF THE CONFERENCE ALGORITMY 2016

ISBN

978-80-227-4544-4

ISSN

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e-ISSN

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Počet stran výsledku

9

Strana od-do

84-92

Název nakladatele

Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry

Místo vydání

Bratislava

Místo konání akce

Vysoké Tatry - Podbanské, Slovakia

Datum konání akce

13. 3. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000391175600009