Extension Operators for Trimmed Spline Spaces

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.

References in corpus (2)

• CutFEM Based on Extended Finite Element Spaces
• Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension

Cited by in corpus (5)

• Robust Trimmed Multipatch IGA with Singular Maps
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• Hybridized Isogeometric Method for Elliptic Problems on CAD Surfaces with Gaps
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• Generalized eigenvalue stabilization for immersed explicit dynamics