Unconditionally optimal time two-mesh mixed finite element algorithm for a nonlinear fourth-order distributed-order time fractional diffusion equation

DOI10.1016/J.PHYSD.2024.134090WikidataQ128526027 ScholiaQ128526027MaRDI QIDQ6496493

Zhichao Fang, Hong Li, Yang Liu, Jin-Feng Wang, Cao Wen

Publication date: 3 May 2024

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

mixed finite element methodtime two-mesh algorithmfourth-order distributed-order time fractional diffusion equationunconditional a priori error analysis

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Miscellaneous topics in partial differential equations (35Rxx)

Cites Work

• Unnamed Item
• Finite element methods based on two families of second-order numerical formulas for the fractional cable model with smooth solutions
• Fast second-order time two-mesh mixed finite element method for a nonlinear distributed-order sub-diffusion model
• Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments
• Numerical analysis for distributed-order differential equations
• Unconditionally optimal error analysis of Crank-Nicolson Galerkin FEMs for a strongly nonlinear parabolic system
• The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation
• Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation
• Mixed methods for fourth-order elliptic and parabolic problems using radial basis functions
• Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation
• Time second-order finite difference/finite element algorithm for nonlinear time-fractional diffusion problem with fourth-order derivative term
• Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
• A two-grid mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with time-fractional derivative
• A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations
• Approximation methods for the distributed order calculus using the convolution quadrature
• Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation
• Unconditionally optimal \(H^1\)-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations
• Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media
• Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order
• A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model
• A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
• Numerical treatment of non-linear fourth-order distributed fractional sub-diffusion equation with time-delay
• TT-M finite element algorithm for a two-dimensional space fractional Gray-Scott model
• A numerical method for distributed order time fractional diffusion equation with weakly singular solutions
• A novel finite volume method for the Riesz space distributed-order advection-diffusion equation
• A high order numerical method and its convergence for time-fractional fourth order partial differential equations
• A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations
• Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
• Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation
• Two alternating direction implicit spectral methods for two-dimensional distributed-order differential equation
• Finite difference/finite element methods for distributed-order time fractional diffusion equations
• Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
• Discretized Fractional Calculus
• Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
• Galerkin–Legendre spectral method for the distributed-order time fractional fourth-order partial differential equation
• Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework
• Optimal convergence analysis of mixed finite element methods for fourth-order elliptic and parabolic problems
• Two families of second-order fractional numerical formulas and applications to fractional differential equations
• A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel
• Unconditional analysis of the linearized second-order time-stepping scheme combined with a mixed element method for a nonlinear time fractional fourth-order wave equation

This page was built for publication: Unconditionally optimal time two-mesh mixed finite element algorithm for a nonlinear fourth-order distributed-order time fractional diffusion equation