The dimension reduction method of two-grid Crank-Nicolson mixed finite element solution coefficient vectors for nonlinear fourth-order reaction diffusion equation with temporal fractional derivative

DOI10.1016/j.cnsns.2024.107962OpenAlexW4392563328MaRDI QIDQ6131379

Yihua Cai, Yihui Zeng, Yuejie Li, Yitian Zeng, Zhen-Dong Luo

Publication date: 5 April 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2024.107962

zbMATH Keywords

proper orthogonal decompositionstability and error estimatenonlinear fourth-order reaction diffusion equation with time-fractional derivativereduced dimension extrapolated two-grid Crank-Nicolson mixed finite element method

Mathematics Subject Classification ID

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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
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• A mixed finite element method for a time-fractional fourth-order partial differential equation
• A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions
• Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations
• Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation
• High-order finite element methods for time-fractional partial differential equations
• Finite element approximation for a modified anomalous subdiffusion equation
• A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions
• Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
• Numerical solution of time fractional Tricomi-type equation by an RBF based meshless method
• Fractional calculus models of complex dynamics in biological tissues
• Multidimensional nonlinear diffusion arising in population genetics
• An efficient technique based on finite difference/finite element method for solution of two-dimensional space/multi-time fractional Bloch-Torrey equations
• Reduced spline method based on a proper orthogonal decomposition technique for fractional sub-diffusion equations
• Numerical solution of time fractional nonlinear Klein-Gordon equation using sinc-Chebyshev collocation method
• A two-grid mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with time-fractional derivative
• A reduced-order finite element method based on proper orthogonal decomposition for the Allen-Cahn model
• The reduced-dimension technique for the unknown solution coefficient vectors in the Crank-Nicolson finite element method for the Sobolev equation
• The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows
• Reduced proper orthogonal decomposition spectral element method for the solution of 2D multi-term time fractional mixed diffusion and diffusion-wave equations in linear and nonlinear modes
• A reduced-order energy-stability-preserving finite difference iterative scheme based on POD for the Allen-Cahn equation
• A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A collocation method for fractional diffusion equation in a long time with Chebyshev functions
• A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations
• A fully coupled multiphase flow and geomechanics solver for highly heterogeneous porous media
• Optimal pointwise-in-time error analysis of a mixed finite element method for a multi-term time-fractional fourth-order equation
• Mixed finite element methods for a fourth order reaction diffusion equation
• Residual based sampling in POD model order reduction of drift-diffusion equations in parametrized electrical networks
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• The dynamics of coherent structures in the wall region of a turbulent boundary layer
• An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Numerical simulation of the temperature field of the stadium building foundation in frozen areas based on the finite element method and proper orthogonal decomposition technique
• A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation
• Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations
• Optimal convergence analysis of mixed finite element methods for fourth-order elliptic and parabolic problems
• Nonlocal solvability of quasilinear degenerate equations with Gerasimov-Caputo derivatives