Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions
type: Item
instance of: scholarly article
title: Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions
zbMATH Open document ID: 1410.65348
author: Fang Liu
author: Zongqi Liang
author: Y. Yan
published in: Journal of Computational and Applied Mathematics
publication date: 2019-03-26T00:00:00Z
full work available at URL: http://hdl.handle.net/10034/621824
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 7042035
zbMATH Keywords: space-fractional partial differential equations
zbMATH Keywords: finite element method
zbMATH Keywords: error estimates
MaRDI profile type: Publication
OpenAlex ID: W2904244000
cites work: Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
cites work: Galerkin finite element approximation of symmetric space-fractional partial differential equations
cites work: Q4233638
cites work: Q3141895
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Chaos, fractional kinetics, and anomalous transport
cites work: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
cites work: Finite difference approximations for fractional advection-dispersion flow equations
cites work: Finite difference methods for two-dimensional fractional dispersion equation
cites work: A second-order accurate numerical approximation for the fractional diffusion equation
cites work: Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
cites work: An algorithm for the numerical solution of two-sided space-fractional partial differential equations
cites work: Variational formulation for the stationary fractional advection dispersion equation
cites work: Least squares finite-element solution of a fractional order two-point boundary value problem
cites work: An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
cites work: Local Discontinuous Galerkin methods for fractional diffusion equations
cites work: Discontinuous Galerkin time stepping method for solving linear space fractional partial differential equations
cites work: A Space-Time Spectral Method for the Time Fractional Diffusion Equation
cites work: Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
cites work: Fourier spectral methods for fractional-in-space reaction-diffusion equations
cites work: A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
cites work: Q3421758
cites work: Q5440446
cites work: A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements
cites work: Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains
cites work: A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain
cites work: Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations
cites work: Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation
cites work: A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
cites work: A tunable finite difference method for fractional differential equations with non-smooth solutions
cites work: An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution
cites work: A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
cites work: Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
cites work: Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations
cites work: High-order numerical methods for solving time fractional partial differential equations
cites work: Numerical analysis of a two-parameter fractional telegraph equation
cites work: A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation
cites work: Regularity of the solution to 1-D fractional order diffusion equations
cites work: Q3994952
cites work: Galerkin Finite Element Methods for Parabolic Problems
Wikidata QID: Q128737652
DOI: 10.1016/J.CAM.2018.12.004
Recommended article: Optimal convergence rates of moving finite element methods for space-time fractional differential equations
Recommended article: Error Estimates for Semidiscrete Finite Element Approximations of Linear and Semilinear Parabolic Equations Under Minimal Regularity Assumptions
Recommended article: Convergence of fractional step mimetic finite difference discretizations for semilinear parabolic problems
Recommended article: Finite element methods for fractional-order diffusion problems with optimal convergence order
Recommended article: Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
Recommended article: Optimal \(H^1\) spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation
Recommended article: Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
Recommended article: Optimal spatial \(H^1\)-norm analysis of a finite element method for a time-fractional diffusion equation
Recommended article: Convergence analysis of moving finite element methods for space fractional differential equations
Recommended article: Fractional order convergence rate estimates of finite difference method on nonuniform meshes
description: scientific article; zbMATH DE number 7042035