Error analysis of a continuous-discontinous Galerkin finite element model for generalized 2D vorticity dynamics

Jacobus J.W. van der Vegt, F. Izsak, Onno Bokhove

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    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 languageUndefined
    Article number10.1137/050633202
    Pages (from-to)1349-1369
    Number of pages21
    JournalSIAM journal on numerical analysis
    Issue number1/4
    Publication statusPublished - 2007


    • MSC-65M12
    • MSC-65M15
    • IR-63793
    • EWI-8497
    • METIS-241867
    • MSC-65M60

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