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Hybrid discontinuous Galerkin methods with relaxed. (English) Zbl 1434.35058

The paper under consideration is the second part of a pair of papers considering Hybrid Discontinuous Galerkin methods with relaxed \(H(\operatorname{div})\)-conformity. The main objective of this second part consists in the presentation of a high order polynomial robust analysis for the relaxed \(H(\operatorname{div})\)-conforming Hybrid Discontinuous Galerkin discretization of the two dimensional Stokes problem. The base for this is given by the polynomial robust LBB-condition for BDM elements proven recently by two of the authors. It is derived by a direct approach instead of using a best approximation result. Furthermore, the impact of the reconstruction operator on the \(hp\) analysis is studied and numerical examples for the polynomial robustness are considered, too. Finally, the authors present an efficient operator splitting time integration scheme fior the Navier-Stokes equations which includes the ideas of the reconstruction operator. The paper is rather comprehensive and self-contained. The bibliography contains 31 items.

MSC:

35Q30 Navier-Stokes equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Software:

NGSolve; Netgen; FEATFLOW
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References:

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