Notes on the convergence order of gradient schemes for time fractional differential equations

DOI10.1016/J.CRMA.2018.02.006zbMath1447.65071OpenAlexW2793119921WikidataQ130175482 ScholiaQ130175482MaRDI QIDQ1747395

Abdallah Bradji

Publication date: 8 May 2018

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.2018.02.006

zbMATH Keywords

numerical solutiontime-fractional diffusion-wave equationgradient discretization method

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Fractional partial differential equations (35R11)

Related Items (6)

SUSHI for a non-linear time fractional diffusion equation with a time independent delay ⋮ An $$L^\infty (H^1)$$-Error Estimate for Gradient Schemes Applied to Time Fractional Diffusion Equations ⋮ A New Gradient Scheme of a Time Fractional Fokker–Planck Equation with Time Independent Forcing and Its Convergence Analysis ⋮ A New Optimal $$L^{\infty }(H^1)$$–Error Estimate of a SUSHI Scheme for the Time Fractional Diffusion Equation ⋮ A Second Order Time Accurate Finite Volume Scheme for the Time-Fractional Diffusion Wave Equation on General Nonconforming Meshes ⋮ A new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equations

Cites Work

• A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
• Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation
• Two mixed finite element methods for time-fractional diffusion equations
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
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• A fully discrete difference scheme for a diffusion-wave system
• Convergence analysis of some first order and second order time accurate gradient schemes for semilinear second order hyperbolic equations
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• Finite volume element method for two-dimensional fractional subdiffusion problems
• Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix–fracture interfaces
• Convergence Order of a Finite Volume Scheme for the Time-Fractional Diffusion Equation
• DGM, an Item of GDM
• An Error Estimate for the Approximation of Linear Parabolic Equations by the Gradient Discretization Method
• Some Convergence Results of a Multi-dimensional Finite Volume Scheme for a Time-Fractional Diffusion-Wave Equation

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