Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- and Divergence-Preserving Operators
| Autor: | Rüdiger Verfürth, Christian Kreuzer, Pietro Zanotti |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Discretization Applied Mathematics Mathematical analysis Order (ring theory) Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Finite element method 010101 applied mathematics Moment (mathematics) Linear map Computational Mathematics Discontinuous Galerkin method Discontinuous galerkin discretization FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Divergence (statistics) Mathematics |
| Zdroj: | Computational Methods in Applied Mathematics. 21:423-443 |
| ISSN: | 1609-9389 1609-4840 |
| DOI: | 10.1515/cmam-2020-0023 |
| Popis: | 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 quasioptimal 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. Ergebnisberichte des Instituts für Angewandte Mathematik;625 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|