α#x02010;robust H1‐norm convergence analysis of L1FEM‐ADI scheme for 2D/3D subdiffusion equation with initial singularity

DOI10.1002/MMA.9442zbMath1529.65020MaRDI QIDQ6183130

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Publication date: 26 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

weak singularity\(\alpha\)-robust\(H^1\)-norm error estimateL1FEM-ADI schemeTFDE

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

Cites Work

• Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation
• Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
• Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
• \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation
• \( \alpha \)-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation
• Pointwise error estimate of an alternating direction implicit difference scheme for two-dimensional time-fractional diffusion equation
• Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations
• A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Blow-up of error estimates in time-fractional initial-boundary value problems
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• A novel compact ADI scheme for the time-fractional subdiffusion equation in two space dimensions

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