Finite Element Methods with B-Splines: Slide Collection (Sample) Klaus H�llig and J�rg H�rner

Terms of Use:
The slide collection is intended only for the use by professors to present lectures based on the SIAM book Finite Element Methods with B-Splines. No permission is granted for any other use, in particular for making the slide collection or parts thereof available to third parties.

• Introduction
• Basic Finite Element Concepts
  • Model Problem
  • Mesh Based Elements
  • Sobolev Spaces
  • Abstract Variational Problems
  • Approximation Error
• B-Splines
  • The Concept of Splines
  • Definition and Basic Properties
  • Recurrence Relation
  • Representation of Polynomials
  • Subdivision
  • Scalar Products
• Finite Element Bases
  • Multivariate B-Splines
  • Splines on Bounded Domains
  • Weight Functions
  • WEB-Splines
  • Hierarchical Bases
• Approximation with Weighted Splines
  • Dual Functions
  • Stability
  • Polynomial Approximation
  • Quasi-Interpolation
  • Boundary Regularity
  • Error Estimates for Standard Weight Functions
• Boundary Value Problems
  • Essential Boundary Conditions
  • Natural Boundary Conditions
  • Mixed Problems with Variable Coefficients
  • Biharmonic Equation
  • Linear Elasticity
  • Plane Strain and Plane Stress
• Multigrid Methods
  • Multigrid Idea
  • Grid Transfer
  • Basic Algorithm
  • Smoothing and Coarse Grid Approximation
  • Convergence
• Implementation
  • Boundary Representation
  • Classification of Grid Cells
  • Evaluation of weight functions
  • Numerical Integration
  • Matrix Assembly
• Appendix

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