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A priori error analysis for finite element approximations of the Stokes problem on dynamic meshes.
- Source :
- IMA Journal of Numerical Analysis; Jan2014, Vol. 34 Issue 1, p123-146, 24p
- Publication Year :
- 2014
-
Abstract
- In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying the backward Euler method for time discretization we use the discrete Helmholtz or Stokes projection to evaluate the solution at time tn−1 on the new spatial mesh at time tn. The theoretical results consist of a priori error estimates that show a dependence on the time step size not better than (1/Δt). These surprisingly pessimistic upper bounds are complemented by numerical examples giving evidence for a negative convergence rate, at least for a large range of time step sizes, and in this sense backing our theory. These observations imply that using adaptive meshes for incompressible flow problems is delicate and requires further investigation. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 02724979
- Volume :
- 34
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- IMA Journal of Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 94184463
- Full Text :
- https://doi.org/10.1093/imanum/drt001