Extension Operators for Trimmed Spline Spaces

TL;DR

This paper introduces a stable extension operator for trimmed spline spaces, enabling improved cut isogeometric methods for elliptic problems through polynomial extension and projection techniques.

Contribution

It presents a novel discrete extension operator for trimmed spline spaces, with proven stability and approximation properties, facilitating advanced isogeometric analysis.

Findings

Proven stability of the extension operator

Effective polynomial extension and projection method

Application to stable cut isogeometric methods

Abstract

We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ 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.