Combined finite volume element method for singularly perturbed reaction-diffusion problems

DOI10.1016/j.amc.2008.10.047zbMath1161.65357OpenAlexW2039192653MaRDI QIDQ1008576

Sutthisak Phongthanapanich, Pramote Dechaumphai

Publication date: 30 March 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2008.10.047

zbMATH Keywords

singular perturbationfinite element methodfinite volume methodnumerical exampleserror estimatereaction-diffusion equationhigh-order schemefinite volume element methodexplicit scheme

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Uses Software

• FEAPpv

Cites Work

• Unnamed Item
• The numerical solution for reaction--diffusion combustion with fuel consumption
• Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type
• Petrov-Galerkin methods for systems of nonlinear reaction-diffusion equations
• Symmetric finite volume discretizations for parabolic problems.
• A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations.
• Studies of the accuracy of time integration methods for reaction-diffusion equations.
• Numerical approach to fast reactions in reaction-diffusion systems: Application to buffered calcium waves in bistable models
• On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
• Multiscale finite element modeling of diffusion-reaction equation using bubble functions with bilinear and triangular elements
• Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions
• Enriched finite element methods for unsteady reaction-diffusion problems
• Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions
• An efficient high-order algorithm for solving systems of reaction-diffusion equations
• Symmetric mixed covolume methods for parabolic problems
• APPROXIMATION BY THE FINITE VOLUME METHOD OF AN ELLIPTIC-PARABOLIC EQUATION ARISING IN ENVIRONMENTAL STUDIES
• Alternating direction finite volume element methods for 2D parabolic partial differential equations
• Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems