Pointwise-in-time a posteriori error control for time-fractional parabolic equations

DOI10.1016/j.aml.2021.107515OpenAlexW3192035000MaRDI QIDQ2236735

Natalia Kopteva

Publication date: 26 October 2021

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

Full work available at URL: https://arxiv.org/abs/2105.05848

zbMATH Keywords

optimal convergence ratesgraded meshes\(L1\) schemefractional-order parabolic equationpointwise-in-time a posteriori error bounds

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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 (6)

A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations ⋮ Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign ⋮ Exact solutions and Hyers-Ulam stability of fractional equations with double delays ⋮ Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations ⋮ Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data

Cites Work

• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
• A posteriori error estimates of spectral Galerkin methods for multi-term time fractional diffusion equations
• Maximum principle for the generalized time-fractional diffusion equation
• The Maximum Principle for Time-Fractional Diffusion Equations and Its Application
• Maximum Norm A Posteriori Error Estimation for Parabolic Problems Using Elliptic Reconstructions
• 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
• 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
• Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations

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