Abstract
A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpolation result, and hp-error estimates for continuous L 2-orthogonal projections.
| Original language | English |
|---|---|
| Pages (from-to) | 1119-1140 |
| Number of pages | 22 |
| Journal | Mathematics of Computation |
| Volume | 76 |
| Issue number | 259 |
| DOIs | |
| Publication status | Published - 1 Jul 2007 |
Keywords
- Continuous interior penalty
- Convection-diffusion
- Hp-finite element method
- Hp-interpolation and projection
- Hp-inverse trace inequality