An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems

Garg, D and Ganesan, S (2022) An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems. In: Applied Numerical Mathematics, 171 . pp. 106-127.

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Abstract

An a priori analysis for a generalized local projection stabilized finite element approximation of the Stokes, and the Darcy flow equations are presented in this paper. A first-order conforming P1c finite element space is used to approximate both the velocity and pressure. It is shown that the stabilized discrete bilinear form satisfies the inf-sup condition in the generalized local projection norm. Moreover, a priori error estimates are established in a mesh-dependent norm as well as in the L2-norm for the velocity and pressure. The optimal and quasi-optimal convergence properties are derived for the Stokes and the Darcy flow problems. Finally, the derived estimates are numerically validated with appropriate examples. © 2021 IMACS

Item Type:	Journal Article
Publication:	Applied Numerical Mathematics
Publisher:	Elsevier B.V.
Additional Information:	The copyright for this article belongs to Elsevier B.V.
Keywords:	Flow of fluids; Stabilization, Darcy's flow; Darcy's problems; Error estimates; Flow problems; Galerkin's approximation; Generalized local projection stabilization; Inf-sup conditions; Local projection stabilizations; Local projections; Stokes problem, Finite element method
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	18 Oct 2021 10:00
Last Modified:	18 Oct 2021 10:00
URI:	http://eprints.iisc.ac.in/id/eprint/70188

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