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

2018/10/10 by Frei, Stefan
#65N12 #65N30 #76D07 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1810.04766

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 L²-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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