We approximate the solution of the Stokes equations by a new quasi-optimal and pressure robust discontinuous Galerkin discretization of arbitrary order. This means quasi-optimality of the velocity error independent of the pressure. Moreover, the discretization is well-defined for any load which is admissible for the continuous problem and it also provides classical quasi-optimal estimates for the sum of velocity and pressure errors. The key design principle is a careful discretization of the load involving a linear operator, which maps discontinuous Galerkin test functions onto conforming ones thereby preserving the discrete divergence and certain moment conditions on faces and elements.
Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- And Divergence-Preserving Operators / C. Kreuzer, R. Verfurth, P. Zanotti. - In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. - ISSN 1609-4840. - (2020 Aug 05). [Epub ahead of print] [10.1515/cmam-2020-0023]
Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- And Divergence-Preserving Operators
P. Zanotti
2020
Abstract
We approximate the solution of the Stokes equations by a new quasi-optimal and pressure robust discontinuous Galerkin discretization of arbitrary order. This means quasi-optimality of the velocity error independent of the pressure. Moreover, the discretization is well-defined for any load which is admissible for the continuous problem and it also provides classical quasi-optimal estimates for the sum of velocity and pressure errors. The key design principle is a careful discretization of the load involving a linear operator, which maps discontinuous Galerkin test functions onto conforming ones thereby preserving the discrete divergence and certain moment conditions on faces and elements.Pubblicazioni consigliate
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