Discrete maximum principles for FE solutions of nonstationary diffusion‐reaction problems with mixed boundary conditions

Abstract: In this paper we derive and discuss sufficient conditions thatprovide the validity of the discrete maximum principle for nonstationarydiffusion-reaction problems with mixed boundary conditions solved by meansof simplicial finite elements and the θ time discretization method. Theoreticalanalysis is supported by numerical experiments. AMS subject classifications: 65M60, 65M50, 35B50Keywords: nonstationarydiffusion-reactionproblem, maximumprinciple, mixedboundary conditions, linear finite elements, discrete maximum principle, simplicialpartition, angle conditionCorrespondenceDepartment of Applied Analysis, E¨otv ¨os Lor´and UniversityH–1518, Budapest, Pf. 120, HungaryInstitute of Mathematics and Statistics, University of West-HungaryErzs´ebet u. 9, H–9400, Sopron, HungaryInstitute of Mathematics, Helsinki University of TechnologyP.O. Box 1100, FIN–02015 TKK, Finlandfaragois@cs.elte.hu, rhorvath@ktk.nyme.hu, sergey.korotov@hut.fiISBN 978-951-22-9510-4 (print)ISBN 978-951-22-9511-1 (PDF)ISSN 0784-3143 (print)ISSN 1797-5867 (PDF)Helsinki University of TechnologyFaculty of Information and Natural SciencesDepartment of Mathematics and Systems AnalysisP.O. Box 1100, FI-02015 TKK, Finlandemail: math@tkk.fi http://math.tkk.fi/

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