抛物问题的基于Crouzeix-Raviart元的有限体积元方法(英文)

Finite Volume Element Method with Crouzeix- Raviart Element for Parabolic Problems

我们考虑了二维抛物问题的基于Crouzeix Raviart元的有限体积元方法.为了得到误差估计,我们引入Ritz投影并研究了它在H1和L2范数意义下的逼近性质.证明了微分方程的真解和有限体积元方程的解在H1和L2范数意义下的误差估计是最优的.

We consider a finite volume element method with the Crouzeix Raviart element for two-dimensional parabolic problem.In order to get the error estimates,we introduce the Ritz projection and study its approximation properties.It is proved that the finite volume element approximation derived are convergent with the optimal order in H^1- and L^2-norm.