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Time stepping procedures for the non-stationary Stokes equations

✍ Scribed by Werner Varnhorn

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
654 KB
Volume
15
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider first and second‐order implicit time stepping procedures for the non‐stationary Stokes equations in bounded domains of ℝ^3^. Using energy estimates we prove the optimal convergence properties in the Sobolev spaces H^m^(G)(m = 0, 1, 2) uniformly in time, provided that the Stokes solution has a certain degree of regularity. Here in the case of the second‐order scheme (method of Crank–Nicholson) the Stokes solution has to satisfy a non‐local compatibility condition at the initial time t = O, which can be satisfied by a special initial construction.

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