Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem

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• 作者：Naveed Ahmed^a ; ^{ahmed@wias-berlin.de} ; Simon Becher^b ; ^{simon.becher@tu-dresden.de} ; Gunar Matthies^b ; ^{gunar.matthies@tu-dresden.de}
• 关键词：65M12 ; 65M15 ; 65M60
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：28-52
• 全文大小：2923 K
• 卷排序：313

文摘

We 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.