In this paper, we introduce two one-parameter families of quadratic polynomial enrichments designed to enhance the accuracy of the classical Crouzeix--Raviart finite element. These enrichments are realized by using weighted line integrals as enriched linear functionals and quadratic polynomial functions as enrichment functions. To validate the effectiveness of our approach, we conduct numerical experiments that confirm the improvement achieved by the proposed method.

翻译：本文提出两种单参数二次多项式富集族，旨在提升经典Crouzeix-Raviart有限元的精度。这些富集通过采用加权线积分作为富集线性泛函，并以二次多项式函数作为富集函数来实现。为验证方法的有效性，我们进行数值实验，结果证实了所提方法带来的精度提升。