\({\boldsymbol{H^1}}\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation

DOI10.1137/22m1506468arXiv2205.06060MaRDI QIDQ6079498

Xu Wu, Chaoyu Quan

Publication date: 29 September 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.06060

zbMATH Keywords

graded meshsubdiffusion equationpositive semidefiniteness\(H^1\)-norm stability and convergenceL2-type method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11) Numerical analysis (65-XX)

Related Items (1)

Long time \(H^1\)-stability of fast \(\mathrm{L}2\)-\(1_\sigma\) method on general nonuniform meshes for subdiffusion equations

Cites Work

• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• A new difference scheme for the time fractional diffusion equation
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Time fractional diffusion: A discrete random walk approach
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• Energy stable L2 schemes for time-fractional phase-field equations
• A sharp \(\alpha\)-robust \(L^\infty (H^1)\) error bound for a time-fractional Allen-Cahn problem discretised by the Alikhanov \(L2-1_\sigma\) scheme and a standard FEM
• Subdiffusion with time-dependent coefficients: improved regularity and second-order time stepping
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint
• Optimal \(H^1\) spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation
• A high-order L2 type difference scheme for the time-fractional diffusion equation
• Optimal spatial \(H^1\)-norm analysis of a finite element method for a time-fractional diffusion equation
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A fully discrete difference scheme for a diffusion-wave system
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• Spectral Methods
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• Spectral Methods in MATLAB
• Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions
• Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem
• A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
• Analysis of adaptive BDF2 scheme for diffusion equations
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: \({\boldsymbol{H^1}}\) -Norm Stability and Convergence of an L2-Type Method on Nonuniform Meshes for Subdiffusion Equation