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

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van der Vegt, J.J.W. and Izsák, F. and Bokhove, O. (2007) Error analysis of a continuous-discontinous Galerkin finite element model for generalized 2D vorticity dynamics. SIAM Journal on Numerical Analysis, 45 (4). pp. 1349-1369. ISSN 0036-1429

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Abstract:Abstract. A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite 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 finite element method for the stream function and a discontinous Galerkin finite element method for the (potential) vorticity. Since this algorithm satisfies 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.
Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/63793
Official URL:http://dx.doi.org/10.1137/050633202
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