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- ItemStabilized finite element schems for incompressible flow using Scott-Vogelius elements(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Burman, Erik; Linke, AlexanderWe propose a stabilized finite element method based on the Scott-Vogelius element in combination with either a local projection stabilization or an edge oriented stabilization based on a penalization of the gradient jumps over element edges. We prove a discrete inf-sup condition leading to optimal a priori error estimates. The theoretical considerations are illustrated by some numerical examples.
- ItemHigher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ahmed, Naveed; Becher, Simon; Matthies, GunarWe introduce and analyze discontinuous Galerkin time discretizations coupled with continuous finite element methods based on equal-order interpolation in space for velocity and pressure in transient Stokes problems. Spatial stability of the pressure is ensured by adding a stabilization term based on local projection. We present error estimates for the semi-discrete problem after discretization in space only and for the fully discrete problem. The fully discrete pressure shows an instability in the limit of small time step length. Numerical tests are presented which confirm our theoretical results including the pressure instability.