Abstract
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on a Nitsche formulation of the interface condition together with a stabilization term. Starting from inf-sup stable spaces on the two meshes, we prove that the resulting composite method is indeed inf-sup stable and as a consequence optimal a priori error estimates hold.
Highlights
Meshing of complex geometries remains a challenging and time consuming task in engineering applications of the finite element method
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces
We focus in particular on composite meshes consisting of one mesh that overlaps another
Summary
Introduction Meshing of complex geometries remains a challenging and time consuming task in engineering applications of the finite element method. The interface conditions on these cut elements are enforced weakly and consistently using Nitsche’s method [1] In this setting [2] first developed and analyzed a composite mesh method for elliptic second order problem based on Nitsche’s method. The Nitsche method approach using cut elements used in this work makes it possible to obtain a consistent and stable formulation while maintaining the conditioning of the algebraic system for both conforming and non-conforming high order finite elements. We consider Stokes flow and devise a method based on a stabilized Nitsche formulation for enforcement of the interface conditions at the border between the two meshes. See [11] for further details
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