Abstract
Abstract. A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin ��?nite element method for the generalized 2D vorticity dynamics equations. These equations describe several types of geophysical flows, including the Euler equations. The algorithm consists of a continuous Galerkin ��?nite element method for the stream function and a discontinous Galerkin ��?nite element method for the (potential) vorticity. Since this algorithm satis��?es a number of invariants, such as energy and enstrophy conservation, it is possible to provide detailed error estimates for this non-linear problem. The main result of the analysis is a reduction in the smoothness requirements on the vorticity field from $H^2(\Omega),$ obtained in a previous analysis, to $W_p^r(\Omega)$ with $r>\frac{1}{p}$ and $p>2.$ In addition, sharper estimates for the dependence of the error on time and numerical examples on a model problem are provided.
Original language | Undefined |
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Article number | 10.1137/050633202 |
Pages (from-to) | 1349-1369 |
Number of pages | 21 |
Journal | SIAM journal on numerical analysis |
Volume | 45 |
Issue number | 1/4 |
DOIs | |
Publication status | Published - 2007 |
Keywords
- MSC-65M12
- MSC-65M15
- IR-63793
- EWI-8497
- METIS-241867
- MSC-65M60