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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 (Engelska)Ingår i: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 21, nr 5-6, s. 1157-1172Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2017. Vol. 21, nr 5-6, s. 1157-1172
Nyckelord [en]
Poroelasticity, Biot system, Fixed-stress split iterative coupling, Contraction mapping, A priori error estimates
Nationell ämneskategori
Matematik
Forskningsämne
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-69245DOI: 10.1007/s10596-017-9691-7ISI: 000415817200022OAI: oai:DiVA.org:kau-69245DiVA, id: diva2:1254263
Konferens
15th European Conference on the Mathematics of Oil Recovery (ECMOR), SEP, 2016, Amsterdam, NETHERLANDS
Tillgänglig från: 2018-10-08 Skapad: 2018-10-08 Senast uppdaterad: 2018-10-19Bibliografiskt granskad

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