\(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation

DOI10.1016/J.APNUM.2021.05.025zbMath1486.65133OpenAlexW3170286454MaRDI QIDQ2041047

Yanyan Li

Publication date: 15 July 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.05.025

zbMATH Keywords

ADI schemeweak singularitytime-fractional diffusion\(\alpha\)-robust\(H^1\)-norm error estimate

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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)

Related Items (6)

A weighted ADI scheme with variable time steps for diffusion-wave equations ⋮ An implicit robust numerical scheme with graded meshes for the modified Burgers model with nonlocal dynamic properties ⋮ Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations ⋮ α#x02010;robust H¹‐norm convergence analysis of L1FEM‐ADI scheme for 2D/3D subdiffusion equation with initial singularity ⋮ Error estimate of L1-ADI scheme for two-dimensional multi-term time fractional diffusion equation ⋮ An implicit difference scheme for the fourth-order nonlinear non-local PIDEs with a weakly singular kernel

Cites Work

• Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
• Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology
• Numerical methods for the two-dimensional multi-term time-fractional diffusion equations
• Conservation laws of \((3+\alpha)\)-dimensional time-fractional diffusion equation
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• A new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equations
• Regularity theory for time-fractional advection-diffusion-reaction equations
• An efficient parallel approximate algorithm for solving time fractional reaction-diffusion equations
• Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials
• A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition
• A discrete comparison principle for the time-fractional diffusion equation
• Sharp \(H^1\)-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
• A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
• Sharp error estimate of a compact \(L1\)-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels
• An application of fractional differential equations to risk theory
• Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation
• Preprocessing schemes for fractional-derivative problems to improve their convergence rates
• A weak Galerkin finite element method for high dimensional time-fractional diffusion equation
• 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

This page was built for publication: \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation