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

DOI10.1002/num.20547zbMath1220.65133OpenAlexW1968805294MaRDI QIDQ2998909

Robert Horváth, Sergey Korotov, István Faragó

Publication date: 11 May 2011

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20547

zbMATH Keywords

maximum principlenumerical experimentsmixed boundary conditionsdiscrete maximum principleCrank-Nicolson schemelinear finite elementssimplicial triangulationbackward Euler discretizationweighted difference schemeangle and time step conditionlinear constant coefficient parabolic equationnonstationary diffusion reaction problem

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Maximum principles in context of PDEs (35B50) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Preserving nonnegativity of an affine finite element approximation for a convection-diffusion-reaction problem ⋮ Qualitative properties of nonlinear parabolic operators ⋮ Unconditionally positivity and boundedness preserving schemes for a FitzHugh–Nagumo equation ⋮ Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their approximations ⋮ Qualitative properties of nonlinear parabolic operators II: the case of PDE systems ⋮ The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations ⋮ Positivity-preserving finite volume difference schemes for atmospheric dispersion models with degenerate vertical diffusion ⋮ A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations ⋮ On some discrete qualitative properties of implicit finite difference solutions of nonlinear parabolic problems ⋮ Qualitative properties of discrete nonlinear parabolic operators

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