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Title: | A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities | Authors: | Radu, Florin Adrian Kumar, Kundan Nordbotten, Jan Martin POP, Sorin |
Issue Date: | 2018 | Source: | IMA JOURNAL OF NUMERICAL ANALYSIS, 38 (2),p. 884-920 | Abstract: | In this work, we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate parabolic equation and an elliptic one. The proposed numerical scheme is based on backward Euler for the temporal discretization and mixed finite element method for the spatial one. A priori stability and error estimates are presented to prove the convergence of the scheme. A monotone increasing, Holder continuous saturation is considered. The convergence of the scheme is naturally dependant on the Holder exponent. The nonlinear systems ¨ within each time step are solved by a robust linearization method, called the L-scheme. This iterative method does not involve any regularization step. The convergence of the L-scheme is rigorously proved under the assumption of a Lipschitz continuous saturation. For the Holder continuous case, a numerical convergence is established. Numerical results (two-dimensional and three-dimensional) are presented to sustain the theoretical findings. | Notes: | Radu, FA (reprint author), Univ Bergen, Dept Math, POB 7800, N-5020 Bergen, Norway. florin.radu@math.uib.no; kundan.kumar@math.uib.no; jan.nordbotten@math.uib.no; sorin.pop@uhasselt.be | Keywords: | linearization; two-phase flow; mixed finite element method; convergence analysis; a priori error estimates; porous media; Richards’ equation; degenerate parabolic problems; coupled problems; holder continuity | Document URI: | http://hdl.handle.net/1942/25850 | ISSN: | 0272-4979 | e-ISSN: | 1464-3642 | DOI: | 10.1093/imanum/drx032 | ISI #: | 000453910300001 | Rights: | © The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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preprint1604.pdf | Non Peer-reviewed author version | 493.3 kB | Adobe PDF | View/Open |
10.1093@imanum@drx032.pdf Restricted Access | Published version | 1.2 MB | Adobe PDF | View/Open Request a copy |
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