Professor of Mathematics at University of California, Irvine

less than 1 minute read

ABSTRACT. This chapter focuses on the geometric decomposition of the $C^m$-conforming finite elements on simplexes in arbitrary dimension constructed by Hu, Lin and Wu. The distance structure is introduced for the simplicial lattice to present a key non-overlapping decomposition of the simplicial lattice, in which each component will be used to determine the normal derivatives at each lower dimensional sub-simplex.

CONTENTS

  1. Distance and Derivative in Simplicial Lattice
    • Simplicial lattices
    • Distance
    • Derivative and distance
  2. Smooth Finite Elements in Two Dimensions
    • Examples in two dimensions
    • Derivatives at vertices
    • Hermite-type finite elements
    • Normal derivatives on edges
  3. Smooth Finite Elements in Arbitrary Dimensions
    • Decompositions of the simplicial lattice
    • Degrees of freedom
    • Smooth finite elements in arbitrary dimension

Chapter 3: Geometric Decomposition of Smooth Finite Elements

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Lagrangedec

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Chapter 3: Geometric Decomposition of Smooth Finite Elements

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