A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation

DOI10.4208/aamm.2014.m693zbMath1499.65517OpenAlexW2467982773MaRDI QIDQ5153646

Wen Chen, Guofei Pang, Kam-Yim Sze

Publication date: 30 September 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.2014.m693

zbMATH Keywords

finite elementfinite differencespace-fractional derivativeadvection-dispersion

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) PDEs with low regular coefficients and/or low regular data (35R05) 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

Enriched reproducing kernel particle method for fractional advection-diffusion equation, Unnamed Item, Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model, Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations, Generalized finite difference method with irregular mesh for a class of three-dimensional variable-order time-fractional advection-diffusion equations, Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations, A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations, Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Gauss-Jacobi-type quadrature rules for fractional directional integrals
• A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• On mean square displacement behaviors of anomalous diffusions with variable and random orders
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• A note on the finite element method for the space-fractional advection diffusion equation
• Fractional-order systems and controls. Fundamentals and applications
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Numerical solution of the space fractional Fokker-Planck equation.
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Finite element solutions for the space fractional diffusion equation with a nonlinear source term
• A second-order accurate numerical approximation for the fractional diffusion equation
• Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
• Finite difference methods for two-dimensional fractional dispersion equation
• An Intuitive Study of Fractional Derivative Modeling and Fractional Quantum in Soft Matter
• An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• Fractional Calculus With Applications in Mechanics
• Fractional Calculus with Applications in Mechanics