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

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arxiv 1806.01062 v2 pith:X4TWOHUX submitted 2018-06-04 math.NA cs.NA

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

Annalisa Buffa , J\"urgen D\"olz , Stefan Kurz , Sebastian Sch\"ops , Rafael V\'azques , Felix Wolf This is my paper
classification math.NA cs.NA
keywords spacesanalysisapproximationelementisogeometricmethodsmultipatchoperators
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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.

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