Chapter 2: Geometric Decomposition of Lagrange Elements
ABSTRACT. This note explores the geometric decomposition of Lagrange elements using barycentric coordinates and the simplicial lattice. The first section introduces the concept of barycentric coordinates, a powerful tool to represent points within a geometric simplex. The second section delves into the simplicial lattice, which is a fundamental concept in this study. In the third section, the note presents the geometric decomposition of Lagrange elements, building upon the concepts of barycentric coordinates and the simplicial lattice.
CONTENTS
- Barycentric Coordinates
- Simplical Lattice
- The simplicial lattice and its geometric embeddings
- Sub-simplicial lattices
- Polynomials and Bernstein basis
- Bubble polynomials
- Geometric Decomposition of Lagrange Elements
Chapter 2: Geometric Decomposition of Lagrange Elements
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