Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results as a basis, we derive new convergence resu...

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Bibliographic Details
Published inNumerische Mathematik Vol. 144; no. 1; pp. 201 - 236
Main Authors Buffa, Annalisa, Dölz, Jürgen, Kurz, Stefan, Schöps, Sebastian, Vázquez, Rafael, Wolf, Felix
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2020
Springer Nature B.V
Subjects
Approximation
Differential equations
Finite element method
Interpolation
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Operators (mathematics)
Simulation
Theoretical
65N12
65N38
65D07
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Summary:We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results as a basis, we derive new convergence results of optimal order w.r.t. the respective energy spaces and provide approximation properties of the spline discretisations of trace spaces for application in the theory of isogeometric boundary element methods. Our analysis allows for a straight forward generalisation to finite element methods.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-019-01079-x