Extension Operators for Trimmed Spline Spaces
Numerical Analysis
2022-11-01 v1 Numerical Analysis
Abstract
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree with continuous derivatives. The construction is based on polynomial extension from neighboring elements together with projection back into the spline space. We prove stability and approximation results for the extension operator. Finally, we illustrate how we can use the extension operator to construct a stable cut isogeometric method for an elliptic model problem.
Cite
@article{arxiv.2205.06543,
title = {Extension Operators for Trimmed Spline Spaces},
author = {Erik Burman and Peter Hansbo and Mats G. Larson and Karl Larsson},
journal= {arXiv preprint arXiv:2205.06543},
year = {2022}
}