Name
Title | ||
|---|---|---|
Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives |
Abstract | ||
|---|---|---|
In this paper we review the existing and develop new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L2 stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1023/A:1015132126817 | J. Sci. Comput. |
Keywords | Field | DocType |
new higher derivative case,error estimate,local discontinuous galerkin methods,stability,local discontinuous galerkin method,post-processing.,higher order derivative,partial differential equations,numerical experiment,discontinuous galerkin method,new result,new local discontinuous galerkin,partial differential equations with higher derivatives,new method,correct interface numerical flux,higher derivative,higher order derivatives,local uniform mesh,convergence,nonlinearity,rate of convergence,partial differential equation,galerkin method,higher order,convection diffusion equation | Discontinuous Galerkin method,Differential equation,Nonlinear system,Mathematical analysis,Galerkin method,Numerical partial differential equations,Partial derivative,Partial differential equation,Multigrid method,Mathematics | Journal |
Volume | Issue | ISSN |
17 | 1-4 | 1573-7691 |
Citations | PageRank | References |
43 | 4.91 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jue Yan | 1 | 198 | 24.23 |
| Chi-Wang Shu | 2 | 4053 | 540.35 |
| d m bushnell | 3 | 43 | 4.91 |