Extension operators for trimmed spline spaces
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 stabili...
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| Published in | Computer methods in applied mechanics and engineering Vol. 403; p. 115707 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.01.2023
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 1879-2138 |
| DOI | 10.1016/j.cma.2022.115707 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 115707 |
| Author | Hansbo, Peter Larson, Mats G. Larsson, Karl Burman, Erik |
| Author_xml | – sequence: 1 givenname: Erik orcidid: 0000-0003-4287-7241 surname: Burman fullname: Burman, Erik email: e.burman@ucl.ac.uk organization: Mathematics, University College London, UK – sequence: 2 givenname: Peter orcidid: 0000-0001-7352-1550 surname: Hansbo fullname: Hansbo, Peter email: peter.hansbo@ju.se organization: Mechanical Engineering, Jönköping University, Sweden – sequence: 3 givenname: Mats G. surname: Larson fullname: Larson, Mats G. email: mats.larson@umu.se organization: Mathematics and Mathematical Statistics, Umeå University, Sweden – sequence: 4 givenname: Karl orcidid: 0000-0001-7838-1307 surname: Larsson fullname: Larsson, Karl email: karl.larsson@umu.se organization: Mathematics and Mathematical Statistics, Umeå University, Sweden |
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| Cites_doi | 10.1016/j.cma.2018.03.022 10.1137/18M1185624 10.1137/20M137937X 10.1016/j.cma.2017.06.004 10.1016/j.cma.2014.10.055 10.1007/s00211-013-0603-z 10.1007/s10915-014-9838-9 10.1002/nme.4823 10.1016/j.cma.2018.03.034 10.1090/S0025-5718-07-01951-5 10.1137/070704435 10.1016/j.jcp.2018.07.020 10.1016/0021-9045(73)90029-4 10.1137/S0036142900373208 10.1016/j.cma.2016.07.006 10.1016/0021-9045(75)90091-X 10.1016/j.cma.2022.114792 10.1016/j.cma.2019.01.030 10.1016/j.cma.2003.12.032 10.1007/s00211-022-01313-z 10.1186/s40323-020-00164-3 10.1007/s00466-019-01796-y 10.1017/S096249291400004X 10.1016/j.crma.2010.10.006 10.1016/j.cma.2017.06.018 10.1007/s11831-017-9220-9 10.1137/19M1244718 10.1007/BF02243847 10.4208/jcm.1802-m2017-0219 10.1016/j.cma.2016.07.040 10.1051/m2an:2006006 10.1007/s00211-012-0497-1 |
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| Keywords | Discrete extension operators Cut isogeometric methods Unfitted finite element methods Trimmed spline spaces |
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| SubjectTerms | 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 |
| Title | Extension operators for trimmed spline spaces |
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