Journal of Scientific Computing
A Discontinuous Spectral Element Model for Boussinesq-Type Equations
Journal of Scientific Computing
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
Local discontinuous Galerkin methods for nonlinear Schrödinger equations
Journal of Computational Physics
High-order Compact Schemes for Nonlinear Dispersive Waves
Journal of Scientific Computing
Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations
Journal of Computational Physics
A (Dis)continuous finite element model for generalized 2D vorticity dynamics
Journal of Computational Physics
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect
Journal of Computational Physics
Numerical studies of the stochastic Korteweg-de Vries equation
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation
Journal of Computational Physics
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics
Multi-symplectic integration of the Camassa-Holm equation
Journal of Computational Physics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
Polymorphic nodal elements and their application in discontinuous Galerkin methods
Journal of Computational Physics
Journal of Scientific Computing
Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs
Journal of Scientific Computing
Journal of Scientific Computing
Local discontinuous Galerkin methods for the generalized Zakharov system
Journal of Computational Physics
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
Journal of Computational Physics
Finite volume schemes for dispersive wave propagation and runup
Journal of Computational Physics
The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation
Journal of Scientific Computing
A numerical study of variable depth KdV equations and generalizations of Camassa-Holm-like equations
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Negative-Order Norm Estimates for Nonlinear Hyperbolic Conservation Laws
Journal of Scientific Computing
A dispersively accurate compact finite difference method for the Degasperis-Procesi equation
Journal of Computational Physics
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Journal of Computational Physics
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In this paper we develop a local discontinuous Galerkin method for solving KdV type equations containing third derivative terms in one and two space dimensions. The method is based on the framework of the discontinuous Galerkin method for conservation laws and the local discontinuous Galerkin method for viscous equations containing second derivatives; however, the guiding principle for intercell fluxes and nonlinear stability is new. We prove L2 stability and a cell entropy inequality for the square entropy for a class of nonlinear PDEs of this type in both one and multiple space dimensions, and we give an error estimate for the linear cases in the one-dimensional case. The stability result holds in the limit case when the coefficients to the third derivative terms vanish; hence the method is especially suitable for problems which are "convection dominated," i.e., those with small second and third derivative terms. Numerical examples are shown to illustrate the capability of this method. The method has the usual advantage of local discontinuous Galerkin methods, namely, it is extremely local and hence efficient for parallel implementations and easy for h-p adaptivity.