Time stepping procedures for the non‐stationary Stokes equations | Zendy

Varnhorn Werner | Zendy

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Time stepping procedures for the non‐stationary Stokes equations

Author(s) -

Varnhorn Werner

Publication year - 1992

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1670150105

Subject(s) - mathematics , sobolev space , bounded function , crank–nicolson method , time stepping , mathematical analysis , stokes problem , stokes flow , convergence (economics) , scheme (mathematics) , geometry , discretization , flow (mathematics) , physics , finite element method , economics , thermodynamics , economic growth

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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