Mathematical Theory of Subdivision: Finite Element and Wavelet Methods

Preface
About the authors
1. Overview of finite element method
Some common governing differential equations 
Basic steps of finite element method 
Element stiffness matrix for a bar 
Element stiffness matrix for single variable 2d element 
Element stiffness matrix for a beam element
References for further reading
2. Wavelets
Wavelet basis functions
Wavelet-Galerkin method 
Daubechies wavelets for boundary and initial value problems 
References for further reading
3. Fundamentals of vector spaces 
Introduction
Vector spaces 
Normed linear spaces 
Inner product spaces 
Banach spaces 
Hilbert spaces 
Projection on finite dimensional spaces
Change of basis - Gram-Schmidt othogonalization process
Riesz bases and frame conditions
References for further reading
4. Operators
Mapping of sets, general concept of functions
Operators
Linear and adjoint operators
Functionals and dual space
Spectrum of bounded linear self-adjoint operator 
Classification of differential operators
Existence, uniqueness and regularity of solution
References
5. Theoretical foundations of the finite element method 
Distribution theory
Sobolev spaces
Variational Method
Nonconforming elements and patch test
References for further reading
6. Wavelet- based methods for differential equations
Fundamentals of continuous and discrete wavelets
Multiscaling
Classification of wavelet basis functions 
Discrete wavelet transform 
Lifting scheme for discrete wavelet transform 
Lifting scheme to customize wavelets 
Non-standard form of matrix and its solution 
Multigrid method
References for further reading
7. Error - estimation
Introduction
A-priori error estimation
Recovery based error estimators 
Residual based error estimators 
Goal oriented error estimators
Hierarchical & wavelet based error estimator
References for further reading
Appendix