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

DOI10.1090/mcom/3550zbMath1442.65381OpenAlexW3015004016MaRDI QIDQ5113662

Dazhi Zhang, Boying Wu, Jia Li, Xiong Meng

Publication date: 15 June 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3550

zbMATH Keywords

local discontinuous Galerkin methodanti-dissipationgeneralized numerical fluxeslinearized KdV equationsnumerical initial condition

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) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (7)

A local discontinuous Galerkin method with generalized alternating fluxes for 2D nonlinear Schrödinger equations ⋮ Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations ⋮ Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation ⋮ Analysis of the local discontinuous Galerkin method with generalized fluxes for one-dimensional nonlinear convection-diffusion systems ⋮ On generalized Gauss-Radau projections and optimal error estimates of upwind-biased DG methods for the linear advection equation on special simplex meshes ⋮ Optimal error estimates of the discontinuous Galerkin method with upwind-biased fluxes for 2D linear variable coefficients hyperbolic equations ⋮ Analysis of generalised alternating local discontinuous Galerkin method on layer-adapted mesh for singularly perturbed problems

Cites Work

• Unnamed Item
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Optimally convergent HDG method for third-order Korteweg-de Vries type equations
• Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems
• Numerical simulation of the stochastic Korteweg-de Vries equation
• Analysis of discontinuous Galerkin methods with upwind-biased fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients
• Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation
• A local discontinuous Galerkin method for the Burgers-Poisson equation
• Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equa\-tions
• Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations
• 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
• Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
• Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• 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
• A new discontinuous Galerkin method, conserving the discreteH²-norm, for third-order linear equations in one space dimension
• A Local Discontinuous Galerkin Method for KdV Type Equations
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation
• Model equations for long waves in nonlinear dispersive systems
• Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension

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