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. Numerical experiments are carried out to support the theoretical findings.
翻译:在本文中,我们研究了Crouzeix-Raviart近似解障碍问题,它在三角剖分的元素中点(即重心)中强制施加障碍约束。我们在自然正则性假设下建立了先验误差估计,这些估计是最优的,并且考虑了一种适用于一般障碍的基-对偶型后验误差估计器的可靠性和效率,并且该估计器仅涉及右手边的数据振荡项。我们进行了数值实验以支持理论结果。