Paper Info
Title
On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations.
Abstract
Inf-sup stable mixed methods for the steady incompressible Stokes equations that relax the divergence constraint are often claimed to deliver locking-free discretizations. However, this relaxation leads to a pressure-dependent contribution in the velocity error, which is proportional to the inverse of the viscosity, thus giving rise to a (different) locking phenomenon. However, a recently proposed modification of the right-hand side alone leads to a discretization that is really locking-free; i.e., its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity. In this contribution, we extend this approach to the transient incompressible Stokes equations, where besides the right-hand side also the velocity time derivative requires an improved space discretization. Semidiscrete and fully discrete a priori velocity and pressure error estimates are derived, which show remarkable robustness properties. Two numerical examples illustrate the superior accuracy of pressure-robust space discretizations in the case of small viscosities.
Year
DOI
Venue
2018
10.1137/17M1112017
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
transient incompressible Stokes equations,mixed finite element methods,locking phenomenon,pressure-robustness,a priori error analysis
Compressibility,Inverse,Discretization,Mathematical analysis,A priori and a posteriori,Viscosity,Time derivative,Robustness (computer science),Finite element method,Mathematics
Journal
Volume
Issue
ISSN
56
1
0036-1429
Citations 
PageRank 
References 
1
0.37
12
Authors
3
Name
Order
Citations
PageRank
Naveed Ahmed117525.40
Alexander Linke29212.29
Christian Merdon3627.33