A nonlinear second order in space correction and maximum principle for diffusion operators

DOI10.1016/j.crma.2014.08.010zbMath1303.65090OpenAlexW2080324111MaRDI QIDQ470143

Christophe Le Potier

Publication date: 11 November 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2014.08.010

zbMATH Keywords

maximum principlediffusion equationnonlinear finite volume method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (9)

A nonlinear correction scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes ⋮ An admissibility and asymptotic-preserving scheme for systems of conservation laws with source term on 2D unstructured meshes ⋮ Weakly monotone finite volume scheme for parabolic equations in strongly anisotropic media ⋮ Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem ⋮ Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure ⋮ A nonlinear correction and local minimum principle for diffusion operators with finite differences ⋮ A Finite Volume Scheme Preserving Maximum Principle for the System of Radiation Diffusion Equations with Three-Temperature ⋮ Unnamed Item ⋮ A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators

Cites Work

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• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
• Non linear schemes for the heat equation in 1D
• A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids

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