Isogeometric analysis for time-fractional partial differential equations

DOI10.1007/s11075-019-00844-1zbMath1450.65123OpenAlexW2995522365WikidataQ126586854 ScholiaQ126586854MaRDI QIDQ2205649

Xindi Hu, Shengfeng Zhu

Publication date: 21 October 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00844-1

zbMATH Keywords

error estimateB-splineisogeometric analysisNURBStime-fractional partial differential equationsdiffusion-wave

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Finite element methods applied to problems in solid mechanics (74S05) Fractional derivatives and integrals (26A33) 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 (6)

On Geometric Inverse Problems in Time-Fractional Subdiffusion ⋮ Modelling, analysis, and numerical methods for a geometric inverse source problem in variable-order time-fractional subdiffusion ⋮ Numerical reconstruction of a discontinuous diffusive coefficient in variable-order time-fractional subdiffusion ⋮ Application of the B-Spline Galerkin approach for approximating the time-fractional Burger's equation ⋮ Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes ⋮ Space-time methods based on isogeometric analysis for time-fractional Schrödinger equation

Uses Software

• GeoPDEs
• FODE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast finite volume methods for space-fractional diffusion equations
• Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation
• A multi-domain spectral method for time-fractional differential equations
• \textsc{GeoPDEs}: a research tool for isogeometric analysis of PDEs
• Isogeometric analysis and proper orthogonal decomposition for parabolic problems
• Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations
• Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
• Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations
• Time fractional diffusion: A discrete random walk approach
• Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Numerical algorithm for the time fractional Fokker-Planck equation
• A fully discrete difference scheme for a diffusion-wave system
• Finite element method for space-time fractional diffusion equation
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
• Isogeometric Analysis
• Mathematical analysis of variational isogeometric methods
• Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
• A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
• Quasi‐Toeplitz splitting iteration methods for unsteady space‐fractional diffusion equations
• Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES

This page was built for publication: Isogeometric analysis for time-fractional partial differential equations