Abstract
We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.
| Original language | English |
|---|---|
| Pages (from-to) | 314-330 |
| Number of pages | 17 |
| Journal | Journal of Scientific Computing |
| Volume | 72 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jul 2017 |
| Externally published | Yes |
Keywords
- Discontinuous Galerkin spectral element method
- Energy stability
- Error bound
- Error growth
- Hyperbolic problems
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Numerical Analysis
- General Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics