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Robust fixed stress splitting for Biot’s equations in heterogeneous media
University of Bergen, Bergen, Norway.
University of Bergen, Bergen, Norway.
University of Bergen, Bergen, Norway; Princeton University, Princeton, NJ, USA.
University of Bergen, Bergen, Norway.
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2017 (English)In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 68, p. 101-108Article in journal (Refereed) Published
Abstract [en]

We study the iterative solution of coupled flow and geomechanics in heterogeneous porous media, modeled by a three-field formulation of the linearized Biot's equations. We propose and analyze a variant of the widely used Fixed Stress Splitting method applied to heterogeneous media. As spatial discretization, we employ linear Galerkin finite elements for mechanics and mixed finite elements (lowest order Raviart Thomas elements) for flow. Additionally, we use implicit Euler time discretization. The proposed scheme is shown to be globally convergent with optimal theoretical convergence rates. The convergence is rigorously shown in energy norms employing a new technique. Furthermore, numerical results demonstrate robust iteration counts with respect to the full range of Lame parameters for homogeneous and heterogeneous media. Being in accordance with the theoretical results, the iteration count is hardly influenced by the degree of heterogeneities.

Place, publisher, year, edition, pages
Amsterdam, Netherlands: Elsevier, 2017. Vol. 68, p. 101-108
Keywords [en]
Linear poroelasticity, Biot's equations, Iterative coupling, Heterogeneous porous media
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-69502DOI: 10.1016/j.aml.2016.12.019ISI: 000397832200016OAI: oai:DiVA.org:kau-69502DiVA, id: diva2:1253824
Available from: 2018-10-06 Created: 2018-10-06 Last updated: 2018-11-01Bibliographically approved

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Kumar, Kundan

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