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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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0945-3245

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Explicit trace inequalities for isogeometric analy

Authors: John A Evans Thomas J R Hughes
Publish Date: 2012/07/10
Volume: 123, Issue: 2, Pages: 259-290
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Abstract

We derive new trace inequalities for NURBSmapped domains In addition to Sobolevtype inequalities we derive discrete trace inequalities for use in NURBSbased isogeometric analysis All dependencies on shape size polynomial degree and the NURBS weighting function are precisely specified in our analysis and explicit values are provided for all bounding constants appearing in our estimates As hexahedral finite elements are special cases of NURBS our results specialize to parametric hexahedral finite elements and our analysis also generalizes to Tsplinebased isogeometric analysis We compare the bounding constants appearing in our explicit trace inequalities with numerically computed optimal bounding constants and we discuss application of our results to a Laplace problem We finish this paper with a brief exploration of socalled patchwise trace inequalities for isogeometric analysis

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