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:在本文件中,我们研究了障碍问题的Crouzix-Raviart近似问题,它给三角定位要素的中点(即中点)造成障碍制约,我们先验错误估计,其中含有自然规律性假设,这是最佳的假设,以及一个用于一般障碍的事后误差估计器的可靠性和效率,它涉及仅来自右侧的数据振荡术语,理论结论得到数字实验的支持。