Explicit Trace Inequalities for Isogeometric Analysis and Parametric Hexahedral Finite Elements

摘要

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, 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 T-spline-based isogeometric analysis.