An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
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We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings.
KeywordsDiscontinuous Galerkin methods Equal-order methods Incompressible Navier-Stokes equations
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- 10.Gopalakrishnan, J., Kanschat, G.: Application of unified DG analysis to preconditioning DG methods. In: Bathe, K.J. (ed.) Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, pp. 1943–1945. Cambridge, MA, USA. Elsevier, Amsterdam (2003) Google Scholar
- 13.Lesaint, P., Raviart, P.A.: On a finite element method for solving the neutron transport equation. In: de Boor, C. (ed.) Mathematical Aspects of Finite Elements in Partial Differential Equations, pp. 89–145. Academic Press, New York (1974) Google Scholar