Finite element methods
A lecture note by Jinchao Xu
Cite the note
To cite this book, please use this bibtex entry:
@book{XuFEM2019, title={The Finite Element Methods}, author={Jinchao Xu}, note={\url{http://www.multigrid.org/wiki}}, year={2019} }
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
 Nonsymmetric and/or indefinite problems
 NonConforming 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