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dc.contributor.authorBoth, Jakub
dc.contributor.authorKumar, Kundan
dc.contributor.authorNordbotten, Jan Martin
dc.contributor.authorPop, Iuliu Sorin
dc.contributor.authorRadu, Florin Adrian
dc.date.accessioned2020-08-13T09:25:38Z
dc.date.available2020-08-13T09:25:38Z
dc.date.issued2019
dc.PublishedBoth J, Kumar K, Nordbotten JM, Pop IS, Radu FA. Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. Lecture Notes in Computational Science and Engineering. 2019;126:49-63eng
dc.identifier.urihttps://hdl.handle.net/1956/23724
dc.description.abstractMathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation. Here the backward Euler method is combined with a mixed finite element method, which results in a stable and locally mass-conservative scheme. At each time step one has to solve a non-linear algebraic system, for which one needs adequate iterative solvers. Finding robust ones is particularly challenging here, since the problems considered are double degenerate (i.e. two type of degeneracies are allowed: parabolic-elliptic and parabolic-hyperbolic). Commonly used schemes, like Newton and Picard, are defined either for non-degenerate problems, or after regularising the problem in the case of degenerate ones. Convergence is guaranteed only if the initial guess is sufficiently close to the solution, which translates into severe restrictions on the time step. Here we discuss an iterative linearisation scheme which builds on the L-scheme, and does not employ any regularisation. We prove its rigorous convergence, which is obtained for Hölder type non-linearities. Finally, we present numerical results confirming the theoretical ones, and compare the behaviour of the proposed scheme with schemes based on a regularisation step.en_US
dc.language.isoengeng
dc.publisherSpringeren_US
dc.titleIterative Linearisation Schemes for Doubly Degenerate Parabolic Equationsen_US
dc.typeConference object
dc.typePeer reviewed
dc.typeJournal article
dc.date.updated2020-02-19T08:35:37Z
dc.description.versionacceptedVersionen_US
dc.rights.holderCopyright Springer Nature Switzerland AG 2019en_US
dc.identifier.doihttps://doi.org/10.1007/978-3-319-96415-7_3
dc.identifier.cristin1657067
dc.source.journalLecture Notes in Computational Science and Engineering
dc.relation.projectNorges forskningsråd: 250223


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