Stabilizer-free weak Galerkin finite element method with second-order accuracy in time for the time fractional diffusion equation

DOI10.1016/j.cam.2022.114407zbMath1492.65270OpenAlexW4280543831WikidataQ113878712 ScholiaQ113878712MaRDI QIDQ2151607

Ning Du, Jie Ma, Fuzheng Gao

Publication date: 5 July 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114407

zbMATH Keywords

error estimatessecond orderfractional diffusion equationstabilizer-free weak Galerkin finite element method

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

Related Items (2)

Weak Galerkin finite element method for linear poroelasticity problems ⋮ A dimensional-splitting weak Galerkin finite element method for 2D time-fractional diffusion equation

Cites Work

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• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Finite difference methods for the time fractional diffusion equation on non-uniform meshes
• Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity
• A new difference scheme for the time fractional diffusion equation
• Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation
• Quadratic spline collocation method for the time fractional subdiffusion equation
• Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
• A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel
• A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation
• Weak Galerkin finite element method with second-order accuracy in time for parabolic problems
• A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations
• A weak Galerkin finite element method for second-order elliptic problems
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• An auxiliary space multigrid preconditioner for the weak Galerkin method
• A preconditioning technique for an all-at-once system from Volterra subdiffusion equations with graded time steps
• A second-order fast compact scheme with unequal time-steps for subdiffusion problems
• Fast solution methods for space-fractional diffusion equations
• Weak Galerkin mixed finite element methods for parabolic equations with memory
• Boundary value problems for the diffusion equation of the variable order in differential and difference settings
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
• A fully discrete difference scheme for a diffusion-wave system
• A modified weak Galerkin finite element method for a class of parabolic problems
• A weak Galerkin finite element method for high dimensional time-fractional diffusion equation
• Mixed finite element algorithm for a nonlinear time fractional wave model
• A finite element method for time fractional partial differential equations
• A new weak Galerkin finite element method for the Helmholtz equation
• Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
• A weak Galerkin mixed finite element method for second order elliptic problems
• Weak Galerkin method for the coupled Darcy–Stokes flow
• A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
• A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem
• A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
• Variational formulation for the stationary fractional advection dispersion equation
• Galerkin Finite Element Methods for Parabolic Problems
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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