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Title: Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-Problem
Nearly all classical inf-sup stable mixed finite element methods for the incompressible Stokes equations are not pressure-robust, i.e., the velocity error is dependent on the pressure. However, recent results show that pressure-robustness can be recovered by a nonstandard discretization of the right-hand side alone. This variational crime introduces a consistency error in the method which can be estimated in a straightforward manner provided that the exact velocity solution is sufficiently smooth. The purpose of this paper is to analyze the pressure-robust scheme with low regularity. The numerical analysis applies divergence-free $H^1$-conforming Stokes finite element methods as a theoretical tool. As an example, pressure-robust velocity and pressure a priori error estimates will be presented for the (first-order) nonconforming Crouzeix-Raviart element. A key feature in the analysis is the dependence of the errors on the Helmholtz projector of the right-hand side data, and not on the entire data term. Numerical examples illustrate the theoretical results.  more » « less
Award ID(s):
1719829
PAR ID:
10057098
Author(s) / Creator(s):
Date Published:
Journal Name:
Mathematics of computation
Volume:
87
ISSN:
1088-6842
Page Range / eLocation ID:
1543-1566
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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