An Algebraic Discrete Maximum Principle in Hilbert Space with Applications to Nonlinear Cooperative Elliptic Systems

DOI10.1137/080729566zbMath1211.65060OpenAlexW1991721788MaRDI QIDQ3584612

Publication date: 30 August 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080729566

zbMATH Keywords

finite element method Hilbert space discrete maximum principle nonlinear elliptic systems

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solutions to equations with nonlinear operators (65J15)

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Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems ⋮ Discrete strong extremum principles for finite element solutions of diffusion problems with nonlinear corrections ⋮ The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations ⋮ Quadratic first integrals of kinetic differential equations ⋮ Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling ⋮ Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity ⋮ Some discrete maximum principles arising for nonlinear elliptic finite element problems ⋮ Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operators ⋮ Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems ⋮ A maximum principle for some nonlinear cooperative elliptic PDE systems with mixed boundary conditions

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