# Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem

@article{Linke2019PressurerobustnessIQ, title={Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem}, author={Alexander Linke and Christian Merdon and Michael Neilan}, journal={ArXiv}, year={2019}, volume={abs/1906.03009} }

Recent analysis of the divergence constraint in the incompressible Stokes/Navier--Stokes problem has stressed the importance of equivalence classes of forces and how it plays a fundamental role for an accurate space discretization. Two forces in the momentum balance are velocity--equivalent if they lead to the same velocity solution, i.e., if and only if the forces differ by only a gradient field. Pressure-robust space discretizations are designed to respect these equivalence classes. One way… Expand

#### 7 Citations

Pressure-robustness for the Stokes equations on anisotropic meshes

- Computer Science, Mathematics
- ArXiv
- 2021

The modified Crouzeix–Raviart method was introduced in [5], and extended to anisotropic meshes in [3, 4], and an insightful new numerical example is provided. Expand

Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading

- Mathematics
- 2021

The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in… Expand

An arbitrary order and pointwise divergence-free finite element scheme for the incompressible 3D Navier-Stokes equations

- Computer Science, Mathematics
- ArXiv
- 2021

A new discretization of the incompressible Navier-Stokes equations using the Lamb identity for the advection term (u · ∇)u and the general idea allows a lot of freedom in the treatment of the non-linear term. Expand

Divergence-preserving reconstructions on polygons and a really pressure-robust virtual element method for the Stokes problem

- Mathematics, Computer Science
- ArXiv
- 2020

It is argued that also divergence-free virtual element methods (VEM) on polygonal meshes are not really pressure-robust as long as the right-hand side is not discretised in a careful manner. Expand

A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes

- Mathematics, Computer Science
- ArXiv
- 2020

The novelty of the present contribution is that the reconstruction approach for the Crouzeix-Raviart method, which has a stable Fortin operator on arbitrary meshes, is combined with results on the interpolation error on anisotropic elements for reconstruction operators of Raviart-Thomas and Brezzi-Douglas-Marini type, generalizing the method to a large class of anisotrop triangulations. Expand

Guaranteed upper bounds for the velocity error of pressure-robust Stokes discretisations

- Computer Science, Mathematics
- ArXiv
- 2020

This paper improves guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact… Expand

Pressure-robust error estimate of optimal order for the Stokes equations on domains with edges

- Mathematics, Computer Science
- ArXiv
- 2020

The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields, which degrades the convergence rates on quasi-uniform meshes and makes anisotropic mesh grading reasonable in order to regain optimal convergence characteristics. Expand

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