Uniform global bounds for solutions of an implicit Voronoi finite volume method for reaction-diffusion problems

DOI10.1007/s00211-014-0604-6zbMath1306.65249OpenAlexW2134637938MaRDI QIDQ740808

Alexander Linke, Annegret Glitzky, André Fiebach

Publication date: 9 September 2014

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-014-0604-6

zbMATH Keywords

convergenceNewton's methoderror boundnonlinear diffusionGagliardo-Nirenberg inequalityMichaelis-Menten-Henri reactionnonlinear reaction-diffusion problemsoptical lithographyVornoi finite volume method

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Chemical kinetics in thermodynamics and heat transfer (80A30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equations, Uniform Estimate of the Relative Free Energy by the Dissipation Rate for Finite Volume Discretized Reaction-Diffusion Systems, A structure preserving scheme for the Kolmogorov-Fokker-Planck equation, Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations, Uniform-in-time bounds for approximate solutions of the drift-diffusion system, Global existence of renormalized solutions to entropy-dissipating reaction-diffusion systems, Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems, Numerical methods to simulate moisture dynamics in fibrous sheet

Uses Software

• PARDISO

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