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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FEM
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...
Geometric Decomposition of H(div) Finite Element
Previously we use Lagrange elements as an example to introduce the simplicial lattice and construction of finite elements based on a decomposition of the sim...
Simplicial Lattice and Lagrange Elements
We use Lagrange elements as an example to introduce the simplicial lattice and construction of finite elements based on a decomposition of the simplicial lat...
Complex
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, ...
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...
Research
Geometric Decomposition of H(div) Finite Element
Previously we use Lagrange elements as an example to introduce the simplicial lattice and construction of finite elements based on a decomposition of the sim...
Simplicial Lattice and Lagrange Elements
We use Lagrange elements as an example to introduce the simplicial lattice and construction of finite elements based on a decomposition of the simplicial lat...
Calculus of Variation
Introduction to Calculus of Variation
Problem Formulation
Convex Analysis
Convex Set
We give an “inside" definition of convexity in which the order structure (not the linearity) plays an important role.