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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Mixed and Galerkin finite element approximation of flow in a linear viscoelastic porous medium
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
JI - Composite materials
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0090" target="_blank" >ED1.1.00/02.0090: NTIS - New Technologies for Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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