FINITE ELEMENTS WITH LOCAL PROJECTION STABILIZATION FOR INCOMPRESSIBLE FLOW PROBLEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Finite element method Stabilization Computational fluid dynamics Error estimates Navier-Stokes Stokes
• 年，卷（期）: 2009,（2）
• 页码范围: 116-147
• 页数: 32页
• 语种: 英文

摘要

In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection tabilization(LPS).These methods preserve the favourable stability and approximation properties of classical residual-based stabilization (RBS) techniques but avoid the strong coupling of velocity and pressure in the stabilization terms.LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods.In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years.We consider the Stokes equations,the Oseen linearization and the Navier-Stokes equations.Furthermore,we apply it to optimal control problems with linear(ized)flow problems,since the symmetry of the stabilization leads to the nice feature that the operations"discretize" and "optimize"commute.