Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Local Discontinuous Galerkin Method for the Camassa-Holm Equation
SIAM Journal on Numerical Analysis
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Journal of Scientific Computing
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In this paper we shall present, for the convection-dominated Sobolev equations, the fully-discrete numerical scheme based on the local discontinuous Galerkin (LDG) finite element method and the third-order explicitly total variation diminishing Runge-Kutta (TVDRK3) time marching. A priori error estimate is obtained for any piecewise polynomials of degree at most k驴1, under the general spatial-temporal restriction. The bounded constant in error estimate is independent of the reciprocal of the diffusion and dispersion coefficients, after removing the effect of smoothness of the exact solution. Finally some numerical results are given to verify the presented conclusion.