Barrier function local and global analysis of an \(L1\) finite element method for a multiterm time-fractional initial-boundary value problem

DOI10.1007/S10915-020-01250-9zbMath1447.65086OpenAlexW3036124783MaRDI QIDQ785558

Xiangyun Meng, Martin Stynes

Publication date: 7 August 2020

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

Full work available at URL: https://doi.org/10.1007/s10915-020-01250-9

zbMATH Keywords

barrier function\(L_1\) schememultiterm time-fractional problem

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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 (10)

A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ A novel discrete fractional Grönwall-type inequality and its application in pointwise-in-time error estimates ⋮ \(H^1\)-analysis of H3N3-\(2_\sigma\)-based difference method for fractional hyperbolic equations ⋮ Local analysis of L1-finite difference method on graded meshes for multi-term two-dimensional time-fractional initial-boundary value problem with Neumann boundary conditions ⋮ A class of anomalous diffusion epidemic models based on CTRW and distributed delay ⋮ Two-grid fully discrete finite element algorithms on temporal graded meshes for nonlinear multi-term time-fractional diffusion equations with variable coefficient ⋮ Optimal pointwise-in-time error analysis of a mixed finite element method for a multi-term time-fractional fourth-order equation ⋮ Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation ⋮ The local discontinuous Galerkin finite element method for a multiterm time-fractional initial-boundary value problem ⋮ Using complete monotonicity to deduce local error estimates for discretisations of a multi-term time-fractional diffusion equation

Cites Work

• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
• Error analysis of a finite difference method on graded meshes for a multiterm time-fractional initial-boundary value problem
• Superconvergence of a finite element method for the multi-term time-fractional diffusion problem
• On the stability of the $L^2$ projection in $H^1(\Omega)$
• Convection-Diffusion Problems
• Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time
• Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions
• 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

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