Name
Title | ||
|---|---|---|
Superconvergence and time evolution of discontinuous Galerkin finite element solutions |
Abstract | ||
|---|---|---|
In this paper, we study the convergence and time evolution of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for conservation laws when upwind fluxes are used. We prove that if we apply piecewise linear polynomials to a linear scalar equation, the DG solution will be superconvergent towards a particular projection of the exact solution. Thus, the error of the DG scheme will not grow for fine grids over a long time period. We give numerical examples of P^k polynomials, with 1= |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jcp.2008.07.010 | J. Comput. Physics |
Keywords | Field | DocType |
linear scalar equation,time evolution,discontinuous galerkin method superconvergence upwind flux projection error estimates,discontinuous galerkin,exact solution,finite element solution,conservation law,long time period,piecewise linear polynomial,dg solution,discontinuous galerkin finite element,dg scheme,projection,discontinuous galerkin method,superconvergence,nonlinear equation,piecewise linear | Discontinuous Galerkin method,Exact solutions in general relativity,Mathematical optimization,Polynomial,Mathematical analysis,Scalar (physics),Superconvergence,Finite element method,Piecewise linear function,Mathematics,Conservation law | Journal |
Volume | Issue | ISSN |
227 | 22 | Journal of Computational Physics |
Citations | PageRank | References |
16 | 1.21 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yingda Cheng | 1 | 201 | 20.27 |
| Chi-Wang Shu | 2 | 4053 | 540.35 |