Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation on Cartesian grids

DOI10.1016/j.apnum.2016.11.007zbMath1355.65114OpenAlexW2551057730MaRDI QIDQ729991

Mahboub Baccouch

Publication date: 23 December 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2016.11.007

zbMATH Keywords

numerical examplesuperconvergencea posteriori error estimatessine-Gordon equationCartesian gridslocal discontinuous Galerkin methodRdau polynomials

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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Initial value problems for systems of linear higher-order PDEs (35G40)

Related Items (14)

Convergence and superconvergence of the local discontinuous Galerkin method for semilinear second-order elliptic problems on Cartesian grids ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Optimal error estimates of the local discontinuous Galerkin method for nonlinear second‐order elliptic problems on Cartesian grids ⋮ Local discontinuous Galerkin method for time variable order fractional differential equations with sub-diffusion and super-diffusion ⋮ A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids ⋮ Optimal superconvergence and asymptotically exact \textit{a posteriori} error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids ⋮ Unnamed Item ⋮ Analysis of local discontinuous Galerkin method for time-space fractional sine-Gordon equations ⋮ Two efficient and reliable a posteriori error estimates for the local discontinuous Galerkin method applied to linear elliptic problems on Cartesian grids

Cites Work

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• Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension
• A posteriori error analysis of the discontinuous Galerkin method for two-dimensional linear hyperbolic conservation laws on Cartesian grids
• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• A local discontinuous Galerkin method for the second-order wave equation
• The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis
• Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Numerical solutions of partial differential equations
• A family of parametric finite-difference methods for the solution of the sine-Gordon equation
• Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
• A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
• A superconvergent local discontinuous Galerkin method for elliptic problems
• A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids
• Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equa\-tions
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions
• A model unified field equation
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Superconvergence of the local discontinuous Galerkin method for linear fourth-order time-dependent problems in one space dimension
• Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem
• A Local Discontinuous Galerkin Method for KdV Type Equations
• Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
• Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments

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