Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension

DOI10.1016/j.cam.2017.11.007zbMath1380.65246OpenAlexW2768356123MaRDI QIDQ679594

Mahboub Baccouch

Publication date: 11 January 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.11.007

zbMATH Keywords

projectionserror estimatesnumerical experimentssuperconvergencesine-Gordon equationlocal discontinuous Galerkin methodnonlinear hyperbolic equation

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) 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)

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Cites Work

• Unnamed Item
• Unnamed Item
• The numerical solution of the nonlinear Klein-Gordon and sine-Gordon equations using the Chebyshev tau meshless method
• Numerical solution of one-dimensional Sine-Gordon equation using high accuracy multiquadric quasi-interpolation
• A local discontinuous Galerkin method for the second-order wave equation
• Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems
• On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes
• Numerical solution of sine-Gordon equation by variational iteration method
• Numerical inverse spectral transform for the periodic sine-Gordon equation: Theta function solutions and their linearized stability
• Modulational and numerical solutions for the steady discrete Sine-Gordon equation in two space dimensions
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Exact and numerical solutions to the perturbed sine-Gordon equation
• Numerical solution of the sine-Gordon equation
• A family of parametric finite-difference methods for the solution of the sine-Gordon equation
• Numerical investigation of the behaviour of solutions of the sine-Gordon equation with a singularity for large \(t\)
• A numerical solution of the sine-Gordon equation using the modified decomposition method
• Numerical solutions of a damped sine-Gordon equation in two space variables
• A superconvergent local discontinuous Galerkin method for elliptic problems
• Discrete singular convolution for the sine-Gordon equation
• Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation
• The local discontinuous Galerkin method for linearized incompressible fluid flow: a review
• Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines
• A numerical solution of the coupled sine-Gordon equation using the modified decomposition method
• A review of the local discontinuous Galerkin (LDG) method applied to elliptic problems
• Numerical solution for series sine-Gordon equations using variational method and finite element approximation
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• A pseudo-spectral method that uses an overlapping multidomain technique for the numerical solution of sine-Gordon equation in one and two spatial dimensions
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• A model unified field equation
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
• Numerical Solution to the Sine-Gordon Equation Defined on the Whole Real Axis
• New modification of the HPM for numerical solutions of the sine-Gordon and coupled sine-Gordon equations
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension
• Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
• Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations
• Superconvergence of the local discontinuous galerkin method applied to the one‐dimensional second‐order wave equation
• Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation
• The generalized finite element method