FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div) ELEMENTS

• 来源期刊: 计算数学（英文版）
• 关键词: Finite element methods Navier-Stokes equations CFD
• 年，卷（期）: 2008,（3）
• 页码范围: 410-436
• 页数: 27页
• 语种: 英文

摘要

We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H(div) conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H(div) finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.