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Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics
Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA; Saudi Arabian Oil Company (Aramco), Dhahran, Saudi Arabia.
Mathematics Institute, University of Bergen, Bergen, Norway.
Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA.
2017 (English)In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 21, no 5-6, p. 1157-1172Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider an iterative coupling scheme for solving a fully discretized Biot system based on the fixed-stress split coupling algorithm. Specifically, we derive a priori error estimates for quantifying the error between the solution obtained at any iterate and the true solution. Our approach is based on studying the equations satisfied by the difference of iterates and utilizing a Banach contraction argument to show that the corresponding scheme is a fixed point iteration. Obtained contraction results are then used to derive theoretical convergence error estimates for the single rate iterative coupling scheme. We compare our numerical computations against the theoretically derived contraction estimates and show a good agreement with theory.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 21, no 5-6, p. 1157-1172
Keywords [en]
Poroelasticity, Biot system, Fixed-stress split iterative coupling, Contraction mapping, A priori error estimates
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-69245DOI: 10.1007/s10596-017-9691-7ISI: 000415817200022OAI: oai:DiVA.org:kau-69245DiVA, id: diva2:1254263
Conference
15th European Conference on the Mathematics of Oil Recovery (ECMOR), SEP, 2016, Amsterdam, NETHERLANDS
Available from: 2018-10-08 Created: 2018-10-08 Last updated: 2018-10-19Bibliographically approved

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Kumar, Kundan

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