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

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

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FREI, 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. 89(10), pp. 407-429. ISSN 0271-2091. eISSN 1097-0363. Available under: doi: 10.1002/fld.4701

@article{Frei2019edgeb-55771, title={An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes}, year={2019}, doi={10.1002/fld.4701}, number={10}, volume={89}, issn={0271-2091}, journal={International Journal for Numerical Methods in Fluids}, pages={407--429}, author={Frei, Stefan} }

2021-12-07T10:14:44Z terms-of-use Frei, Stefan 2021-12-07T10:14:44Z An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes eng 2019 Frei, Stefan 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(h<sup>3/2</sup>) in the energy norm and O(h<sup>5/2</sup>) in the L<sup>2</sup>-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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