Abstract
In this paper, we derive a discontinuous Galerkin finite element formulation for the Stokes equations and a group of stable elements associated with the formulation. We prove that these elements satisfy the new inf–sup condition and can be used to solve incompressible flow problems. Associated with these stable elements, optimal error estimates for the approximation of both velocity and pressure in L 2 norm are obtained for the Stokes problems, as well as an optimal error estimate for the approximation of velocity in a mesh dependent norm.
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Ye, X. Discontinuous Stable Elements for the Incompressible Flow. Advances in Computational Mathematics 20, 333–345 (2004). https://doi.org/10.1023/A:1027363218427
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DOI: https://doi.org/10.1023/A:1027363218427