Finite element methods

A lecture note by Jinchao Xu

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To cite this book, please use this bibtex entry:

    title={The Finite Element Methods},
    author={Jinchao Xu},

Table of contents

    • Sobolev Spaces and Boundary Value Problems
    • Model PDEs and Basic Numerical Methods
    • Finite Difference Method
    • An overview of the finite element method
    • H(grad), H(curl) and H(div) spaces
    • H(grad), H(div) and H(curl) Finite element spaces
    • A Posteriori Error Estimates and Adaptive Finite Element Methods
    • A Generalized Lax Equivalence Theorem: Consistency, Stability and Convergence
    • Non-symmetric and/or indefinite problems
    • Non-Conforming Finite Element Methods
    • Mixed finite element methods for second order elliptic problem
    • Linear elasticity and finite elements
    • Mixed Methods for Stokes equations
    • Discontinuous Galerkin Methods
    • Finite Volume Methods
    • Differential forms and a unified theory of exact sequences
    • Approximation Properties of Neural Network Function Class
    • Deep Neural Networks and Finite Elements
    • Introduction to Finite Element Packages