A virtual class of non-conforming finite elements and its applications to Poisson's equation. (8th March 2022)

• Record Type: Journal Article
• Authors: El-Otmany, Hammou
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 12:Number 2(2022)
• Page Start: 176
• Page End: 190
• Publication Date: 2022-03-08
• Subjects: virtual finite element -- Crouzeix-Raviart element -- interpolation error -- consistency error -- a priori error estimates; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

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.