An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
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- Cockburn, B., Kanschat, G. & Schötzau, D. J Sci Comput (2009) 40: 188. doi:10.1007/s10915-008-9261-1
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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.