An enriched finite element method to fractional advection-diffusion equation

DOI10.1007/s00466-017-1400-9zbMath1429.65171OpenAlexW2601680938WikidataQ113327415 ScholiaQ113327415MaRDI QIDQ1702790

Gregory J. Wagner, Wing Kam Liu, Yanping Lian, Yuping Ying, Shengzhi Luan, Shao-Qiang Tang

Publication date: 28 February 2018

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-017-1400-9

zbMATH Keywords

fractional calculusanomalous diffusionfractional advection-diffusion equationPetrov-Galerkin formulation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Fractional ordinary differential equations (34A08)

Related Items (10)

Enriched reproducing kernel particle method for fractional advection-diffusion equation ⋮ An investigation of radial basis functions for fractional derivatives and their applications ⋮ A high-efficient accurate coupled mesh-free scheme for 2D/3D space-fractional convection-diffusion/Burgers' problems ⋮ A Petrov-Galerkin finite element-meshfree formulation for multi-dimensional fractional diffusion equations ⋮ A scale-dependent finite difference approximation for time fractional differential equation ⋮ A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations ⋮ Generalized finite difference method for a class of multidimensional space-fractional diffusion equations ⋮ Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equations ⋮ A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains ⋮ A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system

Cites Work

• Special issue on ``Fractional PDEs: theory, numerics, and applications
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• Anomalous diffusion modeling by fractal and fractional derivatives
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Least squares finite-element solution of a fractional order two-point boundary value problem
• A Petrov-Galerkin finite element method for the fractional advection-diffusion equation
• Fractional Sobolev spaces via Riemann-Liouville derivatives
• Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• A simple scheme for developing ‘upwind’ finite elements
• Variational formulation for the stationary fractional advection dispersion equation

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