A linearized element-free Galerkin method for the complex Ginzburg-Landau equation

DOI10.1016/j.camwa.2021.03.027OpenAlexW3148487644MaRDI QIDQ2019610

Shuling Li, Xiao-Lin Li

Publication date: 21 April 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.03.027

zbMATH Keywords

convergenceerror analysiselement-free Galerkin methodmeshless methodscomplex Ginzburg-Landau equation

Mathematics Subject Classification ID

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) Ginzburg-Landau equations (35Q56)

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Cites Work

• Unnamed Item
• An efficient fully linearized semi-implicit Galerkin-mixed FEM for the dynamical Ginzburg-Landau equations of superconductivity
• On the stability of the moving least squares approximation and the element-free Galerkin method
• Error estimates for the moving least-square approximation and the element-free Galerkin method in \(n\)-dimensional spaces
• Dissipative solitons. From optics to biology and medicine
• Global well-posedness for the generalized 2D Ginzburg-Landau equation
• Direct meshless local Petrov-Galerkin (DMLPG) method for 2D complex Ginzburg-Landau equation
• Unconditional superconvergent analysis of a linearized finite element method for Ginzburg-Landau equation
• Unconditional superconvergence analysis of a linearized Crank-Nicolson Galerkin FEM for generalized Ginzburg-Landau equation
• Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems
• Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions
• Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain
• An element-free Galerkin method for the obstacle problem
• Three-dimensional complex variable element-free Galerkin method
• Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity
• Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation
• High-order compact ADI method using predictor-corrector scheme for 2D complex Ginzburg-Landau equation
• The improved element-free Galerkin method for three-dimensional elastoplasticity problems
• Convergence analysis of a linearized Crank-Nicolson scheme for the two-dimensional complex Ginzburg-Landau equation
• A linearized Crank–Nicolson–Galerkin FEM for the time‐dependent Ginzburg–Landau equations under the temporal gauge
• A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
• Difference methods for computing the Ginzburg-Landau equation in two dimensions
• The world of the complex Ginzburg-Landau equation
• Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation
• On the Time Splitting Spectral Method for the Complex Ginzburg–Landau Equation in the Large Time and Space Scale Limit
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation
• Element‐free Galerkin methods
• A Spectrally Accurate Algorithm and Analysis for a Ginzburg--Landau Model on Superconducting Surfaces
• An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian
• Unconditional superconvergent analysis of a new mixed finite element method for Ginzburg–Landau equation
• Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

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