Extension operators for trimmed spline spaces

• Published in: Computer methods in applied mechanics and engineering Vol. 403; p. 115707
• Main Authors: Burman, Erik, Hansbo, Peter, Larson, Mats G., Larsson, Karl
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2023; Elsevier BV
• Subjects: A-stable; Approximation results; Cut isogeometric method; Cut isogeometric methods; Discrete extension operator; Discrete extension operators; Extension operators; Finite element method; Functions (mathematics); Operators (mathematics); Piecewise polynomial functions; Polynomials; Spline space; Splines; Stability results; Trimmed spline space; Trimmed spline spaces; Unfitted finite element method; Unfitted finite element methods; Discrete extension operators; Cut isogeometric methods; Unfitted finite element methods; Trimmed spline spaces
• ISSN: 0045-7825; 1879-2138; 1879-2138
• DOI: 10.1016/j.cma.2022.115707

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.