On Nonnegativity Preservation in Finite Element Methods for the Heat Equation with Non-Dirichlet Boundary Conditions

DOI10.1007/978-3-319-72456-0_35zbMath1407.65195OpenAlexW2788165996MaRDI QIDQ4611828

Vidar Thomée, Stig Larsson

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-72456-0_35

zbMATH Keywords

maximum principleDelaunaybackward Eulernonnegativity preservation

Mathematics Subject Classification ID

Heat equation (35K05) Maximum principles in context of PDEs (35B50) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

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Cites Work

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• On preservation of positivity in some finite element methods for the heat equation
• On positivity and maximum-norm contractivity in time stepping methods for parabolic equations
• On Positivity Preservation in Some Finite Element Methods for the Heat Equation
• Failure of the discrete maximum principle for an elliptic finite element problem
• On the existence of maximum principles in parabolic finite element equations
• Galerkin Finite Element Methods for Parabolic Problems
• Matrix Iterative Analysis

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