$L2-1_\sigma$ Finite Element Method for Time-Fractional Diffusion Problems with Discontinuous Coefficients
DOI10.4208/eajam.2022-178.101022zbMath1527.65096MaRDI QIDQ6139021
Unnamed Author, Yunqing Huang, Yanping Chen
Publication date: 18 December 2023
Published in: Unnamed Author (Search for Journal in Brave)
Reaction-diffusion equations (35K57) 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)
Cites Work
- Unnamed Item
- A new difference scheme for the time fractional diffusion equation
- Numerical approximation of an interface problem for fractional in time diffusion equation
- Homotopy perturbation method to space-time fractional solidification in a finite slab
- Galerkin finite element methods for parabolic problems
- Finite element methods and their convergence for elliptic and parabolic interface problems
- Long memory processes and fractional integration in econometrics
- Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
- Convergence of a linearized second-order BDF-FEM for nonlinear parabolic interface problems
- The role of fractional calculus in modeling biological phenomena: a review
- 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
- Sharp \(H^1\)-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
- Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods
- A local discontinuous Galerkin method for time-fractional diffusion equation with discontinuous coefficient
- Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations
- Optimal spatial \(H^1\)-norm analysis of a finite element method for a time-fractional diffusion equation
- Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
- The finite element method for elliptic equations with discontinuous coefficients
- Two-grid methods for semilinear interface problems
- An exact solution to the moving boundary problem with fractional anomalous diffusion in drug release devices
- Numerical Analysis of Nonlinear Subdiffusion Equations
- A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
- Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
- Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time
- A Linearised Three-Point Combined Compact Difference Method with Weighted Approximation for Nonlinear Time Fractional Klein-Gordon Equations
- A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
- A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations
- Blow-up of error estimates in time-fractional initial-boundary value problems
- Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy
- A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem
- 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
- Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations
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