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

• Published in: Numerische 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
• Language: English
• 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

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...