Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0036142901390378 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
kdv type equations,derivative term,limit case,linear case,stability result,kdv-type equation,local discontinuous galerkin method,l2 stability,nonlinear stability,discontinuous galerkin method,cell entropy inequality,dimensional case,kdv type,inviscid flow,galerkin method,fluid mechanics,finite element analysis,applied mathematics,stability,kdv equation,conservation | Discontinuous Galerkin method,Second derivative,Nonlinear system,Mathematical analysis,Galerkin method,Finite element method,Numerical analysis,Third derivative,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
40 | 2 | 0036-1429 |
Citations | PageRank | References |
95 | 13.61 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jue Yan | 1 | 198 | 24.23 |
| Chi-Wang Shu | 2 | 4053 | 540.35 |