An indirect finite element method for variable-coefficient space-fractional diffusion equations and its optimal-order error estimates

DOI10.1007/s42967-019-00037-6zbMath1449.65331OpenAlexW2973471320WikidataQ127252573 ScholiaQ127252573MaRDI QIDQ2289882

Xiangcheng Zheng, Vincent J. Ervin, Hong Wang

Publication date: 27 January 2020

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-019-00037-6

zbMATH Keywords

finite element methodfractional diffusion equationconvergence estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05) Approximation by polynomials (41A10) Fractional partial differential equations (35R11)

Related Items

Analysis and discretization for an optimal control problem of a variable-coefficient Riesz-fractional diffusion equation with pointwise control constraints, Finite difference/finite element method for two-dimensional time-space fractional Bloch-Torrey equations with variable coefficients on irregular convex domains, Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval, Error estimate of finite element approximation for two-sided space-fractional evolution equation with variable coefficient, Probability-conservative simulation for \textit{Lévy} financial model by a mixed finite element method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• A second order finite difference-spectral method for space fractional diffusion equations
• Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations
• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations
• Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
• A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations
• Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach
• Error estimates of spectral Galerkin methods for a linear fractional reaction-diffusion equation
• Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
• Spectral Methods
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• Regularity of the solution to 1-D fractional order diffusion equations
• Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
• Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations
• Variational formulation for the stationary fractional advection dispersion equation
• Variational formulation of problems involving fractional order differential operators
• The random walk's guide to anomalous diffusion: A fractional dynamics approach