A finite element semi-Lagrangian explicit Runge-Kutta-Chebyshev method for convection dominated reaction-diffusion problems

DOI10.1016/S0377-0427(02)00746-XzbMath1029.65114MaRDI QIDQ1874191

Rodolfo Bermejo, Mofdi El-Amrani

Publication date: 22 May 2003

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

zbMATH Keywords

performancenumerical examplesconvergence stabilityconvection dominated reaction-diffusion problemssemi-Lagrangian explicit Runge-Kutta-Chebyshev 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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Uses Software

• RKC

Cites Work

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• Analysis of an algorithm for the Galerkin-characteristic method
• Convergence properties of the Runge-Kutta-Chebyshev method
• Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
• RKC: An explicit solver for parabolic PDEs
• On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
• Convection-Dominated Nonlinear Systems: Analysis of the Douglas–Russell Transport-Diffusion Algorithm Based on Approximate Characteristics and Invariant Regions
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• Analysis of a class of quasi-monotone and conservative semi-Lagrangian advection schemes
• Explicit Runge-Kutta methods for parabolic partial differential equations

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