Title: A virtual class of non-conforming finite elements and its applications to Poisson's equation

Authors: Hammou El-Otmany

Addresses: Engineering Sciences Laboratory, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben-Abdellah University Fez, Morocco

Abstract: In this paper, we develop and analyse the virtual class of non-conforming finite element inspired from the classical Crouzeix-Raviart element in two and three-dimensions. We focus on Poisson's equation for theoretical and numerical results. We show that the discrete problem is stable and the a priori error estimates are optimal. Two numerical tests are presented to demonstrate the theoretical results.

Keywords: virtual finite element; Crouzeix-Raviart element; interpolation error; consistency error; a priori error estimates.

DOI: 10.1504/IJMMNO.2022.10045640

International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.2, pp.176 - 190

Received: 14 Dec 2020
Accepted: 30 May 2021

Published online: 08 Apr 2022 *

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