@article{59bf4ad36f554d5c89ea3a2496ec2cea,
title = "Using high-order transport theorems for implicitly defined moving curves to perform quadrature on planar domains",
abstract = "The numerical integration over a planar domain that is cut by an implicitly defined boundary curve is an important problem that arises, for example, in unfitted finite element methods and in isogeometric analysis on trimmed computational domains. In this paper, we introduce a a very general version of the transport theorem for moving domains defined by implicitly defined curves and use it to establish an efficient and accurate quadrature rule for this class of domains. In numerical experiments it is shown that the method achieves high orders of convergence. Our approach is suited for high-order geometrically unfitted finite element methods as well as for high-order trimmed isogeometric analysis.",
keywords = "Fictitious domain methods, Immersed methods, Isogeometric analysis, Numerical quadrature, Transport theorem, Trimming, Unfitted finite element method",
author = "Felix Scholz and Bert J{\"u}ttler",
note = "Funding Information: \ast Received by the editors May 28, 2020; accepted for publication (in revised form) April 26, 2021; published electronically August 5, 2021. https://doi.org/10.1137/20M1341283 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the authors was supported by the ERC Advanced Grant CHANGE, GA 694515. \dagger Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, A-4040 Linz, Austria (felix.scholz@ricam.oeaw.ac.at). \ddagger Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, A-4040 Linz, Austria, and Institute of Applied Geometry, Johannes Kepler University, A-4040 Linz, Austria (bert.juettler@jku.at). Publisher Copyright: Copyright {\textcopyright} by SIAM.",
year = "2021",
doi = "10.1137/20M1341283",
language = "English",
volume = "59",
pages = "2138--2162",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}