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We will analyze the characteristics of Scott-Vogelius finite elements on singular vertices, which cause spurious pressures on solving Stokes equations. A simple postprocessing will be suggested to remove those spurious pressures.
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ($k ge 4$).
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 o
The $H^m$-conforming virtual elements of any degree $k$ on any shape of polytope in $mathbb R^n$ with $m, ngeq1$ and $kgeq m$ are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case $k
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular integral equation o
A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all el