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.
CITATION STYLE
Johansson, A., Larson, M. G., & Logg, A. (2015). High order cut finite element methods for the Stokes problem. Advanced Modeling and Simulation in Engineering Sciences, 2(1). https://doi.org/10.1186/s40323-015-0043-7
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