A New Optimal $$L^{\infty }(H^1)$$–Error Estimate of a SUSHI Scheme for the Time Fractional Diffusion Equation

DOI10.1007/978-3-030-43651-3_27zbMath1454.65074OpenAlexW3034369484MaRDI QIDQ5117450

Abdallah Bradji

Publication date: 25 August 2020

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-43651-3_27

zbMATH Keywords

a priori estimatetime-fractional diffusion equationSUSHI\(L^\infty (H^1)\)-error estimate

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (3)

Convergence analysis of a finite volume scheme for a distributed order diffusion equation ⋮ 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

Cites Work

• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• The gradient discretisation method
• Notes on the convergence order of gradient schemes for time fractional differential equations
• Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.
• A new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equations
• A finite element approximation for a class of Caputo time-fractional diffusion equations
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A second order time accurate SUSHI method for the time-fractional diffusion equation
• Finite volume schemes for the biharmonic problem on general meshes
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Convergence Order of a Finite Volume Scheme for the Time-Fractional Diffusion Equation

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