Analysis on a Finite Volume Element Method for Stokes Problems

为 Stokes 问题的有限体积元素方法被考虑。我们使用一一致的片为速度和片的一个好格子上的明智的线性功能为压力的一个粗糙的格子上的明智的经常的元素。为一般三角测量，我们证明有限的卷元素方法和一个僵绳点的等价是问题， inf 啜条件和近似解决方案的唯一。我们也给最佳的顺序 H1 标准错误估计。为我们给 L2 标准的二个广泛地使用的双网孔，错误估计情况，它在一个是最佳的并且在另一种情况中伪最佳。最后，我们给一个数字例子。

Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example.