In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. The theoretical findings are supported by numerical experiments.

翻译：本文研究了障碍问题的Crouzeix-Raviart逼近，该方法在三角剖分单元的中点（即重心）处施加障碍约束。我们在自然正则性假设下建立了先验误差估计，该估计是最优的；并针对一般障碍问题，建立了仅涉及右端项数据振荡项的原-对偶型后验误差估计子的可靠性与有效性。理论结果得到了数值实验的支持。