Chapter 3: Geometric Decomposition of Smooth Finite Elements
ABSTRACT. This chapter focuses on the geometric decomposition of the $C^m$-conforming finite elements on simplexes in arbitrary dimension constructed by Hu, ...
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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 int...
Chapter 1: Basics on Finite Elements
ABSTRACT. This lecture notes covers the construction of finite element spaces, focusing on simplicial triangulations. Examples of finite elements, such as th...
Finite Element Complex
The epidemic has been going on for more than two years. During this period, one of my main research interests has been finite element complexes. Through a se...
Convex Set
We give an “inside" definition of convexity in which the order structure (not the linearity) plays an important role.