Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System

Local discontinuous Galerkin methods for nonlinear dispersive equations

We develop local discontinuous Galerkin (DG) methods for solving nonlinear dispersive partial differential equations that have compactly supported traveling waves solutions, the so-called ‘‘compactons’’. The schemes we present extend the previous works of Yan and Shu on approximating solutions for linear dispersive equations and for certain KdV-type equations. We present two classes of DG metho...

Local discontinuous Galerkin methods for nonlinear Schrödinger equations

In this paper we develop a local discontinuous Galerkin method to solve the generalized nonlinear Schrödinger equation and the coupled nonlinear Schrödinger equation. L stability of the schemes are obtained for both of these nonlinear equations. Numerical examples are shown to demonstrate the accuracy and capability of these methods. 2004 Elsevier Inc. All rights reserved. MSC: 65M60; 35Q55

Discontinuous Galerkin methods for nonlinear elasticity

Local discontinuous Galerkin methods for elliptic problems

In this paper, we review the development of local discontinuous Galerkin methods for elliptic problems. We explain the derivation of these methods and present the corresponding error estimates; we also mention how to couple them with standard conforming finite element methods. Numerical examples are displayed which confirm the theoretical results and show that the coupling works very well. Copy...

Local discontinuous Galerkin methods for the Cahn-Hilliard type equations

In this paper we develop local discontinuous Galerkin (LDG) methods for the fourth-order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is proved for the general nonlinear case. Numerical examples for the Cahn-Hilliard equation and the Cahn-Hilliard system in one and two dimensions are presented and the numerical results illustrate the accuracy and capabili...