Preprint
Numerical Methods for Non-Stationary Stokes Flow
Zusammenfassung
We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.
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@article{urn:nbn:de:hebis:34-2008051921622,
author={Varnhorn, Werner},
title={Numerical Methods for Non-Stationary Stokes Flow},
year={2008}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2008$n2008 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008051921622 3000 Varnhorn, Werner 4000 Numerical Methods for Non-Stationary Stokes Flow / Varnhorn, Werner 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008051921622=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 08, 03 7136 ##0##urn:nbn:de:hebis:34-2008051921622
2008-05-19T12:37:58Z 2008-05-19T12:37:58Z 2008 urn:nbn:de:hebis:34-2008051921622 http://hdl.handle.net/123456789/2008051921622 194122 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Euler Method Stokes Resolvent Potentials BEM 510 Numerical Methods for Non-Stationary Stokes Flow Preprint We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method. open access Varnhorn, Werner Mathematische Schriften Kassel ;; 08, 03 35J05 35K22 41A30 65M10 76D07 Mathematische Schriften Kassel 08, 03
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