Analysis of a Multi-Term Variable-Order Time-Fractional Diffusion Equation and Its Galerkin Finite Element Approximation
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Publication:5090521
DOI10.4208/jcm.2102-m2020-0211OpenAlexW4281729640WikidataQ114021190 ScholiaQ114021190MaRDI QIDQ5090521
Xiangcheng Zheng, Hongfei Fu, Huan Liu
Publication date: 20 July 2022
Published in: Journal of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/jcm.2102-m2020-0211
Galerkin finite elementvariable-ordermulti-term time-fractional diffusion equationparareal methodsolution regularity
Smoothness and regularity of solutions to PDEs (35B65) 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) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
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- Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications
- A parareal method for time-fractional differential equations
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
- The Galerkin finite element method for a multi-term time-fractional diffusion equation
- On mean square displacement behaviors of anomalous diffusions with variable and random orders
- Galerkin finite element methods for parabolic problems
- A generalized Gronwall inequality and its application to a fractional differential equation
- Variable order differential equations with piecewise constant order-function and diffusion with changing modes
- Parareal algorithms with local time-integrators for time fractional differential equations
- Variable order and distributed order fractional operators
- A preconditioned fast parareal finite difference method for space-time fractional partial differential equation
- Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcing
- Fast algorithm based on TT-M FE system for space fractional Allen-Cahn equations with smooth and non-smooth solutions
- A fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshes
- Wellposedness and smoothing properties of history-state-based variable-order time-fractional diffusion equations
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Finite difference/spectral approximations for the time-fractional diffusion equation
- A fully discrete difference scheme for a diffusion-wave system
- Wellposedness and regularity of the variable-order time-fractional diffusion equations
- Résolution d'EDP par un schéma en temps «pararéel »
- Spectral Methods
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- Regularity of the solution to 1-D fractional order diffusion equations
- Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations
- Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions
- Alternating Direction Implicit Schemes for the Two-Dimensional Time Fractional Nonlinear Super-Diffusion Equations
- An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Subdiffusion with a time-dependent coefficient: Analysis and numerical solution
- Spectral Methods
- Stochastic models for fractional calculus
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
