Mixed and Galerkin finite element approximation of flow in a linear viscoelastic porous medium

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F13%3A43918774" target="_blank" >RIV/49777513:23520/13:43918774 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cma.2013.03.003" target="_blank" >http://dx.doi.org/10.1016/j.cma.2013.03.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2013.03.003" target="_blank" >10.1016/j.cma.2013.03.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mixed and Galerkin finite element approximation of flow in a linear viscoelastic porous medium

Popis výsledku v původním jazyce

We propose two fully discrete mixed and Galerkin finite element approximation to a system of equations describing the slow flow of a slightly compressible single phase fluid in a viscoelastic porous medium. One of our schemes is the natural one for the backward Euler time discretization but, due to the viscoelasticity, seems to be stable only for small enough time steps. The other scheme contains a lagged term in the viscous stress and pressure evolution equations and this is enough to prove unconditional stability. For this lagged scheme we prove an optimal order a priori error estimate under ideal regularity assumptions and demonstrate the convergence rates by using a model problem with a manufactured solution. The model and numerical scheme that wepresent are a natural extension to 'poroviscoelasticity' of the poroelasticity equations and scheme studied by Philips and Wheeler in (for example) [Philip Joseph Philips, Mary F. Wheeler, Comput. Geosci. 11 (2007) 145 - 158] although - i

Název v anglickém jazyce

Mixed and Galerkin finite element approximation of flow in a linear viscoelastic porous medium

Popis výsledku anglicky

We propose two fully discrete mixed and Galerkin finite element approximation to a system of equations describing the slow flow of a slightly compressible single phase fluid in a viscoelastic porous medium. One of our schemes is the natural one for the backward Euler time discretization but, due to the viscoelasticity, seems to be stable only for small enough time steps. The other scheme contains a lagged term in the viscous stress and pressure evolution equations and this is enough to prove unconditional stability. For this lagged scheme we prove an optimal order a priori error estimate under ideal regularity assumptions and demonstrate the convergence rates by using a model problem with a manufactured solution. The model and numerical scheme that wepresent are a natural extension to 'poroviscoelasticity' of the poroelasticity equations and scheme studied by Philips and Wheeler in (for example) [Philip Joseph Philips, Mary F. Wheeler, Comput. Geosci. 11 (2007) 145 - 158] although - i

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

JI - Kompositní materiály

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0090" target="_blank" >ED1.1.00/02.0090: NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

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Svazek periodika

260

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

78-91

Kód UT WoS článku

000320218500006

EID výsledku v databázi Scopus

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