Two one-parameter families of nonconforming enrichments of the Crouzeix-Raviart finite element

TL;DR

This paper introduces two new one-parameter families of quadratic enrichments for the Crouzeix-Raviart finite element, using weighted line integrals and quadratic functions to improve accuracy, validated through numerical experiments.

Contribution

The paper presents novel quadratic polynomial enrichments for the Crouzeix-Raviart element, enhancing its accuracy with a new enrichment approach based on weighted line integrals.

Findings

Improved accuracy demonstrated through numerical experiments

Enrichments effectively enhance the classical Crouzeix-Raviart element

New enrichment functions based on quadratic polynomials

Abstract

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.