On optimal convergence rates for higher-order Navier-Stokes approximations. I. Error estimates for the spatial discretization |
| |
Authors: | Bause Markus |
| |
Institution: |
Institut für Angewandte Mathematik der Universität Erlangen-Nürnberg, Martensstrasse 3, 91058 Erlangen, Germany
|
| |
Abstract: | ** Email: bause{at}am.uni-erlangen.de Due to the increasing use of higher-order methods in computationalfluid dynamics, the question of optimal approximability of theNavierStokes equations under realistic assumptions onthe data has become important. It is well known that the regularitycustomarily hypothesized in the error analysis for parabolicproblems cannot be assumed for the NavierStokes equations,as it depends on non-local compatibility conditions for thedata at time t = 0, which cannot be verified in practice. Takinginto account this loss of regularity at t = 0, improved convergenceof the order (min{h(5/2),h3/t(1/4)+}), for any >0, is shown locally in time for the spatial discretization ofthe velocity field by (non-)conforming finite elements of third-orderapproximability properties. The error estimate itself is provedby energy methods, but it is based on sharp a priori estimatesfor the NavierStokes solution in fractional-order spacesthat are derived by semigroup methods and complex interpolationtheory and reflect the optimal regularity of the solution ast 0. |
| |
Keywords: | Navier Stokes equations finite-element method optimal regularity error estimate |
本文献已被 Oxford 等数据库收录! |
|