Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data
DOI10.1007/s13540-022-00023-5zbMath1503.65236arXiv1809.02015OpenAlexW4224289151WikidataQ114017041 ScholiaQ114017041MaRDI QIDQ2110889
Xiaoping Xie, Binjie Li, Hao Luo
Publication date: 23 December 2022
Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.02015
Laplace transformweak solutiondiscontinuous Galerkin methodoptimal error estimatelow regularitytime fractional subdiffusion
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Laplace transform (44A10) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence
- Time-stepping error bounds for fractional diffusion problems with non-smooth initial data
- Too much regularity may force too much uniqueness
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- A compact finite difference scheme for the fractional sub-diffusion equations
- Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation
- Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation
- An introduction to Sobolev spaces and interpolation spaces
- Numerical solution via Laplace transforms of a fractional order evolution equation
- Some time stepping methods for fractional diffusion problems with nonsmooth data
- Optimal error analysis of a FEM for fractional diffusion problems by energy arguments
- Error estimates of high-order numerical methods for solving time fractional partial differential equations
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Analysis of the L1 scheme for fractional wave equations with nonsmooth data
- A space-time finite element method for fractional wave problems
- Analysis of a temporal discretization for a semilinear fractional diffusion equation
- Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations
- Regularity of solutions to time fractional diffusion equations
- Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data
- Time-stepping discontinuous Galerkin methods for fractional diffusion problems
- A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
- A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term
- Weighted average finite difference methods for fractional diffusion equations
- Two high-order time discretization schemes for subdiffusion problems with nonsmooth data
- A finite element method for time fractional partial differential equations
- Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation
- REGULARITY OF SOLUTIONS TO A TIME-FRACTIONAL DIFFUSION EQUATION
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
- Time discretization of parabolic problems by the discontinuous Galerkin method
- Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
- An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data
- Analysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth Data
- An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
- Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
- Weighted Inequalities of Hardy Type
- A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
- Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Variational formulation for the stationary fractional advection dispersion equation
- Galerkin Finite Element Methods for Parabolic Problems
- Mittag-Leffler Functions, Related Topics and Applications