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

by   Philip L. Lederer, et al.

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 pressure. A Prager-Synge type result relates the errors of divergence-free primal and H(div)-conforming dual mixed methods (for the velocity gradient) with an equilibration constraint that needs special care when discretised. To relax the constraints on the primal and dual method, a more general result is derived that enables the use of a recently developed mass conserving mixed stress discretisation to design equilibrated fluxes that yield pressure-independent guaranteed upper bounds for any pressure-robust (but not necessarily divergence-free) primal discretisation. Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costs of the error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1.



There are no comments yet.


page 1

page 2

page 3

page 4


Pressure-robust staggered DG methods for the Navier-Stokes equations on general meshes

In this paper, we design and analyze staggered discontinuous Galerkin me...

A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes

In a recent work [10], we have introduced a pressure-robust Hybrid High-...

Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity

We present analysis of two lowest-order hybridizable discontinuous Galer...

An EMA-balancing, pressure-robust and Re-semi-robust reconstruction method for unsteady incompressible Navier-Stokes equations

Proper EMA-balance (E: kinetic energy; M: momentum; A: angular momentum)...

A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits

In this paper we propose a novel staggered discontinuous Galerkin method...

Minimal order H(div)-conforming velocity-vorticity approximations for incompressible fluids

We introduce a novel minimal order hybrid Discontinuous Galerkin (HDG) a...

An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow

We propose an augmented Lagrangian preconditioner for a three-field stre...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.