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

Stefan Frei

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arXiv · 1810.04766

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

Stefan Frei

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Abstract

In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain, with the only condition that a maximum angle is fulfilled in each element.This discretisation is motivated by applications on moving domains as arising e.g. in fluid-structure interaction or multiphase-flow problems. To deal with the anisotropies, we define a modification of the original Continuous Interior Penalty stabilisation approach. We show analytically the discrete stability of the method and convergence of order ${\cal O}(h^{3/2})$ in the energy norm and ${\cal O}(h^{5/2})$ in the $L^2$-norm of the velocities. We present numerical examples for a linear Stokes problem and for a non-linear fluid-structure interaction problem, that substantiate the analytical results and show the capabilities of the approach.

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Stefan Frei. 2018-10-10. An edge-based pressure stabilisation technique for finite elements on arbitrarily anisotropic meshes. https://arxiv.org/abs/1810.04766

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