Abstract
We design consistent discontinuous Galerkin finite element schemes for the approximation of the Euler-Korteweg and the Navier-Stokes-Korteweg systems. We show that the scheme for the Euler-Korteweg system is energy and mass conservative and that the scheme for the Navier-Stokes-Korteweg system is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to viscous effects, that is, there is no numerical dissipation. In this sense the methods is consistent with the energy dissipation of the continuous PDE systems.
| Original language | English |
|---|---|
| Pages (from-to) | 2071-2099 |
| Number of pages | 29 |
| Journal | Mathematics of Computation |
| Volume | 83 |
| Early online date | 8 Jan 2014 |
| DOIs | |
| Publication status | Published - 2014 |
Bibliographical note
30 pages, 6 figures, 3 tablesKeywords
- math.NA
- 65M60, 76T10
Fingerprint
Dive into the research topics of 'Energy consistent DG methods for the Navier-Stokes-Korteweg system'. Together they form a unique fingerprint.Profiles
-
Tristan Pryer
- Institute for Mathematical Innovation (IMI) - Director of the Bath Institute for Mathematical Innovation
- Centre for Therapeutic Innovation
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- IAAPS
- Department of Mathematical Sciences - Professor
Person: Research & Teaching, Core staff, Affiliate staff, Teaching & Other