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A locally modified finite element method for a Stokes interface problem

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2025

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Judakova, Gozel
Richter, Thomas

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https://doi.org/10.3934/acse.2025004
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Deutsche Forschungsgemeinschaft (DFG): 548064929

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Advances in Computational Science and Engineering. American Institute of Mathematical Sciences (AIMS). 2025, 3, S. 46-73. eISSN 2837-1739. Verfügbar unter: doi: 10.3934/acse.2025004

Zusammenfassung

In this work, we analyze a stationary Stokes interface problem. For discretization we apply locally modified second-order finite elements for the velocities combined with piecewise constant elements for pressure. The locally modified second-order finite element method is based on a fixed structured coarse mesh, which is then internally resolved and adjusted to the interface by means of a reference element mapping. This corresponds to a sub-triangulation of the coarse mesh into (possibly) anisotropic triangles. We show the stability of the P2 − P0 elements by using the macroelement technique, which requires local stability and a relatively weak global stability. In one particular case, we need to add a local stabilization term, or alternatively to move a critical vertex of the mesh by a small ϵ. Furthermore, we prove optimal error estimates in the energy norm and the L2-norm of the velocity and show detailed numerical results.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Stokes interface problem, inf-sup condition, macroelement technique, a priori error estimation, parametric finite elements

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ISO 690FREI, Stefan, Gozel JUDAKOVA, Thomas RICHTER, 2025. A locally modified finite element method for a Stokes interface problem. In: Advances in Computational Science and Engineering. American Institute of Mathematical Sciences (AIMS). 2025, 3, S. 46-73. eISSN 2837-1739. Verfügbar unter: doi: 10.3934/acse.2025004
BibTex
@article{Frei2025local-73042,
  title={A locally modified finite element method for a Stokes interface problem},
  year={2025},
  doi={10.3934/acse.2025004},
  volume={3},
  journal={Advances in Computational Science and Engineering},
  pages={46--73},
  author={Frei, Stefan and Judakova, Gozel and Richter, Thomas}
}
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