A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations

DOI10.1007/s11075-020-00978-7zbMath1473.65221OpenAlexW3066631337MaRDI QIDQ2028023

Mingfa Fei, Guoyu Zhang, Nan Wang, Cheng-Ming Huang

Publication date: 31 May 2021

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

Full work available at URL: https://doi.org/10.1007/s11075-020-00978-7

zbMATH Keywords

convergence analysisfinite element methodfractional Klein-Gordon equationlinearized scheme

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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)

Related Items (5)

Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations ⋮ Numerical approach for solving two dimensional fractal-fractional PDEs using peridynamic method ⋮ Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation ⋮ Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation ⋮ Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation

Uses Software

• iFEM
• FODE

Cites Work

• Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation
• A new difference scheme for the time fractional diffusion equation
• Numerical algorithm with high spatial accuracy for the fractional diffusion-wave equation with von Neumann boundary conditions
• A fully discrete spectral method for the nonlinear time fractional Klein-Gordon equation
• A compact difference scheme for the fractional diffusion-wave equation
• Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
• Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis
• A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions
• Galerkin finite element methods for parabolic problems
• Numerical solution of a nonlinear Klein-Gordon equation
• The fundamental solutions for the fractional diffusion-wave equation
• A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations
• An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations
• An efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equation
• Unconditional convergence in maximum-norm of a second-order linearized scheme for a time-fractional Burgers-type equation
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
• A compact difference scheme for a two dimensional nonlinear fractional Klein-Gordon equation in polar coordinates
• Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation
• Fast algorithm based on TT-M FE system for space fractional Allen-Cahn equations with smooth and non-smooth solutions
• Unconditionally convergent numerical method for the two-dimensional nonlinear time fractional diffusion-wave equation
• Meshless numerical analysis of a class of nonlinear generalized Klein-Gordon equations with a well-posed moving least squares approximation
• A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation
• Finite difference/finite element methods for distributed-order time fractional diffusion equations
• A weighted ADI scheme for subdiffusion equations
• A fully discrete difference scheme for a diffusion-wave system
• Two finite difference schemes for time fractional diffusion-wave equation
• On the stability of the $L^2$ projection in $H^1(\Omega)$
• Some temporal second order difference schemes for fractional wave equations
• Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation
• Fractional diffusion and wave equations
• Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
• A high‐order compact scheme for the nonlinear fractional <scp>K</scp>lein–<scp>G</scp>ordon equation
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• Time decay for the nonlinear Klein-Gordon equation

This page was built for publication: A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations