Existence of solution of a finite volume scheme preserving maximum principle for diffusion equations

DOI10.1002/num.22184zbMath1384.65078OpenAlexW2734594650MaRDI QIDQ4603190

Yunlong Yu, Guang-Wei Yuan

Publication date: 19 February 2018

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

Full work available at URL: https://doi.org/10.1002/num.22184

zbMATH Keywords

maximum principleexistencenumerical examplesfinite volume schemediffusion equationsdiscontinuous diffusion coefficientsstar shaped polygonal meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) PDEs with low regular coefficients and/or low regular data (35R05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (20)

Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle ⋮ A finite volume scheme preserving the invariant region property for the coupled system of FitzHugh-Nagumo equations on distorted meshes ⋮ The finite volume scheme preserving maximum principle for diffusion equations with discontinuous coefficient ⋮ Discrete strong extremum principles for finite element solutions of diffusion problems with nonlinear corrections ⋮ Unconditionally stable exponential time differencing schemes for the mass‐conserving <scp>Allen–Cahn</scp> equation with nonlocal and local effects ⋮ A nonlinear convex combination in the construction of finite volume scheme satisfying maximum principle ⋮ A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes ⋮ An extremum‐preserving finite volume scheme for three‐temperature radiation diffusion equations ⋮ A new positive finite volume scheme for two‐dimensional convection‐diffusion equation ⋮ A finite volume method preserving maximum principle for the diffusion equations with imperfect interface ⋮ A Finite Volume Scheme Preserving Maximum Principle for the System of Radiation Diffusion Equations with Three-Temperature ⋮ An improvement of the two-point flux approximation scheme on polygonal meshes ⋮ Unnamed Item ⋮ A finite volume scheme preserving maximum principle with cell-centered and vertex unknowns for diffusion equations on distorted meshes ⋮ A Nonlinear Finite Volume Element Method Satisfying Maximum Principle for Anisotropic Diffusion Problems on Arbitrary Triangular Meshes ⋮ A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations ⋮ A positivity-preserving finite volume scheme for three-temperature radiation diffusion equations ⋮ Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes ⋮ Analysis of the nonlinear scheme preserving the maximum principle for the anisotropic diffusion equation on distorted meshes ⋮ Extremum-Preserving Correction of the Nine-Point Scheme for Diffusion Equation on Distorted Meshes

Cites Work

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• A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes
• Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
• Minimal stencil finite volume scheme with the discrete maximum principle
• Finite volume schemes for diffusion equations: Introduction to and review of modern methods
• A Second-Order Maximum Principle Preserving Finite Volume Method for Steady Convection-Diffusion Problems

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