Superconvergence error estimate of a finite element method on nonuniform time meshes for reaction-subdiffusion equations

DOI10.1007/s10915-020-01290-1zbMath1452.65247OpenAlexW3046513723MaRDI QIDQ2007021

Zhimin Zhang, Jincheng Ren, Hong-lin Liao

Publication date: 12 October 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01290-1

zbMATH Keywords

finite element methodsuperconvergencefractional reaction-subdiffusion equationssharp temporal \(H^1\)-norm error estimatetime-space error splitting argument

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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 (9)

L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation ⋮ Two-grid finite element methods for nonlinear time-fractional parabolic equations ⋮ Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data ⋮ On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations ⋮ A fast linearized Galerkin finite element method for the nonlinear multi-term time fractional wave equation ⋮ Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations ⋮ Unconditionally optimal \(H^1\)-error estimate of a fast nonuniform \(\mathrm{L}2-1_\sigma\) scheme for nonlinear subdiffusion equations ⋮ Fast high-order difference scheme for the modified anomalous subdiffusion equation based on fast discrete sine transform ⋮ Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation

Uses Software

• FODE

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