Isogeometric discretizations of the Stokes problem on trimmed geometries
Abstract
The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary conditions a challenging problem. A very popular strategy is to rely on the so-called Nitsche method \cite{MR3264337}. We show that the Nitsche method lacks stability in some degenerate trimmed domain configurations, potentially polluting the computed solutions. After extending the stabilization procedure of \cite{MR4155233} to incompressible flow problems, we show that we recover the well-posedness of the formulation and, consequently, optimal a priori error estimates. Numerical experiments illustrating stability and converge rates are included.
Keywords
Cite
@article{arxiv.2012.15582,
title = {Isogeometric discretizations of the Stokes problem on trimmed geometries},
author = {Riccardo Puppi},
journal= {arXiv preprint arXiv:2012.15582},
year = {2022}
}