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Calcolo

, 55:19 | Cite as

A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem

  • E. Bänsch
  • F. Karakatsani
  • C. G. Makridakis
Article
  • 107 Downloads

Abstract

This work is devoted to a posteriori error analysis of fully discrete finite element approximations to the time dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix–Raviart and Taylor–Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that is hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in \(L^\infty (L^2) \) for the velocity error.

Keywords

A posteriori error estimators Time dependent Stokes Reconstruction Adaptivity Mesh change Crouzeix–Raviart element 

Mathematics Subject Classification

65M15 65M50 65N15 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Mathematics IIIErlangenGermany
  2. 2.Department of Mathematics, Faculty of Science and Engineering, Thornton Science ParkUniversity of ChesterInce, ChesterUK
  3. 3.Modelling and Sc. Computing, DMAMUniversity of CreteHeraklionGreece
  4. 4.Institute for Applied and Computational Mathematics, FORTHHeraklionGreece
  5. 5.MPSUniversity of SussexBrightonUK

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