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Discrete maximum principles for FE solutions of nonstationary diffusion‐reaction problems with mixed boundary conditions
Author(s) -
Faragó István,
Horváth Róbert,
Korotov Sergey
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20547
Subject(s) - mathematics , discretization , partial differential equation , boundary value problem , diffusion , boundary (topology) , maximum principle , partial derivative , reaction–diffusion system , mathematical analysis , mathematical optimization , thermodynamics , physics , optimal control
In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011