Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems

DOI10.3934/dcdsb.2018104zbMath1407.65165OpenAlexW2793325180MaRDI QIDQ1756972

Mahboub Baccouch

Publication date: 28 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018104

zbMATH Keywords

local discontinuous Galerkin method KdV equationsstability a priori error estimates superconvergence Gauss-Radau projections

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (1)

Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations

Cites Work

• Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension
• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• 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
• Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
• Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• A superconvergence result for discontinuous Galerkin methods applied to elliptic problems.
• Parallel adaptive \(hp\)-refinement techniques for conservation laws
• A superconvergent local discontinuous Galerkin method for elliptic problems
• Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
• Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation
• A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids
• The local discontinuous Galerkin method for linearized incompressible fluid flow: a review
• A review of the local discontinuous Galerkin (LDG) method applied to elliptic problems
• A hybridized discontinuous Galerkin method for the nonlinear Korteweg-de Vries equation
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
• Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Riemann Solvers, the Entropy Condition, and Difference
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• A Local Discontinuous Galerkin Method for KdV Type 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
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• Optimal a Posteriori Error Estimates of the Local Discontinuous Galerkin Method for Convection-Diffusion Problems in One Space Dimension
• On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems
• Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
• Model equations for long waves in nonlinear dispersive systems
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