Startseite Error Analysis of the Vector Penalty-Projection Methods for the Time-Dependent Stokes Equations with Open Boundary Conditions
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Error Analysis of the Vector Penalty-Projection Methods for the Time-Dependent Stokes Equations with Open Boundary Conditions

  • Rima Cheaytou ORCID logo EMAIL logo und Philippe Angot
Veröffentlicht/Copyright: 14. November 2024

Abstract

We present in this paper a rigorous error analysis of the vector penalty-projection method for solving the time-dependent incompressible Stokes equations with open boundary conditions on part of the boundary. First, we prove the stability of the scheme. Then we provide an error analysis for the second-order vector penalty-projection method which shows that the convergence rate of the error on the velocity and the pressure is of order 2 in l ( L 2 ( Ω ) ) and l 2 ( L 2 ( Ω ) ) respectively. In addition, it is shown that the splitting errors of the method varies as O ( ε ) , where 𝜀 is a penalty parameter chosen as small as desired. Several numerical tests in agreement with the theoretical results are presented. To the best of our knowledge, this paper provides the first rigorous proof of optimal error estimates for second-order splitting schemes with open boundary conditions.

MSC 2020: 65M12; 35Q30; 35Q35; 76D05

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Received: 2023-12-05
Revised: 2024-10-11
Accepted: 2024-10-27
Published Online: 2024-11-14
Published in Print: 2025-04-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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