Superconvergence of a finite element method for the multi-term time-fractional diffusion problem
From MaRDI portal
Publication:2291930
DOI10.1007/S10915-019-01115-WzbMath1447.65078OpenAlexW3000311770MaRDI QIDQ2291930
Publication date: 31 January 2020
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-019-01115-w
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 (28)
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity ⋮ A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions ⋮ 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 ⋮ A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation ⋮ \textit{A posteriori} error estimates based on superconvergence of FEM for fractional evolution equations ⋮ A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions ⋮ \(\alpha\)-robust error analysis of two nonuniform schemes for subdiffusion equations with variable-order derivatives ⋮ Superconvergence analysis of finite element methods for the variable-order subdiffusion equation with weakly singular solutions ⋮ On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations ⋮ Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian ⋮ Numerical Methods for Solving the Robin Boundary Value Problem for a Generalized Diffusion Equation with a Non-smooth Solution ⋮ Two-grid \(H^1 \)-Galerkin mixed finite elements combined with \(L1\) scheme for nonlinear time fractional parabolic equations ⋮ Two-grid fully discrete finite element algorithms on temporal graded meshes for nonlinear multi-term time-fractional diffusion equations with variable coefficient ⋮ An efficient numerical scheme and its analysis for the multiterm time‐fractional convection‐diffusion‐reaction equation ⋮ On conservative, positivity preserving, nonlinear FV scheme on distorted meshes for the multi-term nonlocal Nagumo-type equations ⋮ Optimal pointwise-in-time error analysis of a mixed finite element method for a multi-term time-fractional fourth-order equation ⋮ Finite difference/finite element method for two-dimensional time-space fractional Bloch-Torrey equations with variable coefficients on irregular convex domains ⋮ Optimal \(H^1\) spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation ⋮ An \(\alpha \)-robust finite element method for a multi-term time-fractional diffusion problem ⋮ Numerical approximation of 2D multi-term time and space fractional Bloch-Torrey equations involving the fractional Laplacian ⋮ \( \alpha \)-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation ⋮ Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel ⋮ A transformed \(L 1\) method for solving the multi-term time-fractional diffusion problem ⋮ \(\beta\)-robust superconvergent analysis of a finite element method for the distributed order time-fractional diffusion equation ⋮ Barrier function local and global analysis of an \(L1\) finite element method for a multiterm time-fractional initial-boundary value problem ⋮ A weak Galerkin finite element method on temporal graded meshes for the multi-term time fractional diffusion equations ⋮ Using complete monotonicity to deduce local error estimates for discretisations of a multi-term time-fractional diffusion equation
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
- Geometric theory of semilinear parabolic equations
- Error analysis of a finite difference method on graded meshes for a multiterm time-fractional initial-boundary value problem
- Optimal spatial \(H^1\)-norm analysis of a finite element method for a time-fractional diffusion equation
- On the stability of the $L^2$ projection in $H^1(\Omega)$
- Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
- The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
- Finite Elements
- 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
- Galerkin Finite Element Methods for Parabolic Problems
- Unnamed Item
This page was built for publication: Superconvergence of a finite element method for the multi-term time-fractional diffusion problem
