Explicit Trace Inequalities for Isogeometric Analysis and Parametric Hexahedral Finite Elements

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2011
Accession Number
ADA555335

Entities

People

  • John Andrew Evans
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Construction
  • Electronic Mail
  • Engineering
  • Equations
  • Finite Element Analysis
  • Functions (Mathematics)
  • Galerkin Method
  • Geometry
  • Inequalities
  • Integrals
  • Mathematics
  • Polynomials
  • Simulations
  • Three Dimensional
  • Two Dimensional
  • Weighting Functions

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Mathematical Modeling and Probability Theory.