Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations
Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations
复制标题
DOI：
10.1051/m2an/2015047
复制
发表时间：
2015-05
期刊：
影响因子：
--
通讯作者：
H. Notsu;M. Tabata
中科院分区：
文献类型：
--
作者：
H. Notsu;M. Tabata
对Navier-Stokes方程的稳定化Lagrange-Galerkin格式证明了具有最优收敛阶的误差估计。该格式是Lagrange-Galerkin方法和Brezzi- Pitkaranta稳定化方法的组合。它保持了两种方法的优点：（i）它对对流占优的问题是鲁棒的，并且要求解的线性方程组是对称的。(ii)由于P1有限元用于速度和压力，因此自由度的数量远小于方程的其他典型单元的数量，例如，P2/P1。因此，该格式是有效的，特别是对三维问题。通过二维和三维计算，理论上的收敛阶数得到了确认。
Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi- Pitkaranta's stabilization method. It maintains the adva ntages of both methods; (i) It is robust for convection- dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient espe- cially for three-dimensional problems. The theoretical convergence orders are recognized numerically by two- and three-dimensional computations.