Multipatch Approximation of the de Rham Sequence and its Traces in Isogeometric Analysis

TL;DR

This paper develops a conforming B-spline discretisation of the de Rham complex on multipatch geometries, providing new convergence results and approximation properties for isogeometric analysis and boundary element methods.

Contribution

It introduces and analyzes interpolation operators that commute with surface differential operators, enabling optimal convergence and trace space approximation in isogeometric analysis.

Findings

Optimal order convergence in energy spaces

New approximation properties for trace spaces

Framework applicable to finite element methods

Abstract

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 straightforward generalisation to finite element methods.