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An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes

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2019

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https://doi.org/10.1002/fld.4701
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International Journal for Numerical Methods in Fluids. Wiley-Blackwell. 2019, 89(10), pp. 407-429. ISSN 0271-2091. eISSN 1097-0363. Available under: doi: 10.1002/fld.4701

Zusammenfassung

In this paper, we analyze a stabilized equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a subdomain, for example, along the boundary of the domain, with the only condition that a maximum angle is fulfilled in each element. This discretization is motivated by applications on moving domains as arising, for example, in fluid-structure interaction or multiphase-flow problems. To deal with the anisotropies, we define a modification of the original continuous interior penalty stabilization approach. We show analytically the discrete stability of the method and convergence of order O(h3/2) in the energy norm and O(h5/2) in the L2-norm of the velocities. We present numerical examples for a linear Stokes problem and for a nonlinear fluid-structure interaction problem, which substantiate the analytical results and show the capabilities of the approach.

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510 Mathematik

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ISO 690FREI, Stefan, 2019. An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes. In: International Journal for Numerical Methods in Fluids. Wiley-Blackwell. 2019, 89(10), pp. 407-429. ISSN 0271-2091. eISSN 1097-0363. Available under: doi: 10.1002/fld.4701
BibTex
@article{Frei2019edgeb-55771,
  year={2019},
  doi={10.1002/fld.4701},
  title={An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes},
  number={10},
  volume={89},
  issn={0271-2091},
  journal={International Journal for Numerical Methods in Fluids},
  pages={407--429},
  author={Frei, Stefan}
}
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