ON THE P1 POWELL-SABIN DIVERGENCE-FREE FINITE ELEMENT FOR THE STOKES EQUATIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Powell Sabin triangles Mixed finite elements Stokes Divergence-free element
• 年，卷（期）: 2008,（3）
• 页码范围: 456-470
• 页数: 15页
• 语种: 英文

摘要

The stability of the P1-P0 mixed-element is established on general Powell-Sabin triangular grids. The piecewise linear finite element solution approximating the velocity is divergence-free pointwise for the Stokes equations. The finite element solution approximating the pressure in the Stokes equations can be obtained as a byproduct if an iterative method is adopted for solving the discrete linear system of equations. Numerical tests are presented confirming the theory on the stability and the optimal order of convergence for the P1 Powell-Sabin divergence-free finite element method.