Construction of a high quality characteristics finite element method

最近，我们发展了一种求解Navier-Stokes方程的稳定特征有限元格式。它是特征线法和稳压法相结合的方案。导出的线性方程组的矩阵是对称的，并且使用了廉价的P1/P1单元。因此，该格式是有效的，特别是对于三维问题。证明了该格式的稳定性和收敛性。误差估计是最优的。因此，该格式除了具有计算上的优势外，还具有数学上的可靠性。在本研究期间，还获得了一些与特征线法相关的数值和理论结果。

Recently we have developed a stabilized characteristics finite element scheme for the Navier-Stokes equations. It is a combined scheme with the characteristics method and a pressure-stabilization method. The matrix of the derived system of linear equations is symmetric and a cheap P1/P1 element is employed. The scheme is, therefore, efficient especially three-dimensional problems.Stability and convergence of the scheme have been proved. The error estimates are optimal. Consequently, the scheme has mathematical reliability in addition to the computational advantages.Some other numerical and theoretical results related to the characteristics method have been obtained in this research period.