Generalized local projection stabilized nonconforming finite element methods for Darcy equations

Garg, D and Ganesan, S (2021) Generalized local projection stabilized nonconforming finite element methods for Darcy equations. In: Numerical Algorithms .

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Abstract

An a priori analysis for a generalized local projection stabilized finite element solution of the Darcy equations is presented in this paper. A first-order nonconforming �1nc finite element space is used to approximate the velocity, whereas the pressure is approximated using two different finite elements, namely piecewise constant � and piecewise linear nonconforming �1nc elements. The considered finite element pairs, �1nc/�0 and �1nc/�1nc, are inconsistent and incompatibility, respectively, for the Darcy problem. The stabilized discrete bilinear form satisfies an inf-sup condition with a generalized local projection norm. Moreover, a priori error estimates are established for both finite element pairs. Finally, the validation of the proposed stabilization scheme is demonstrated with appropriate numerical examples. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Item Type:	Journal Article
Publication:	Numerical Algorithms
Publisher:	Springer
Additional Information:	The copyright for this article belongs to Springer
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	04 Aug 2021 11:50
Last Modified:	04 Aug 2021 11:50
URI:	http://eprints.iisc.ac.in/id/eprint/69061

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