$$ \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\normalvec}{\boldsymbol{n}} \newcommand{\x}{\boldsymbol{x}} \newcommand{\X}{\boldsymbol{X}} \renewcommand{\v}{\boldsymbol{v}} \newcommand{\V}{\boldsymbol{V}} \newcommand{\dfc}{\alpha} % diffusion coefficient \newcommand{\If}{\mathcal{I}_s} % for FEM \newcommand{\Ifb}{{I_b}} % for FEM \newcommand{\sequencei}[1]{\left\{ {#1}_i \right\}_{i\in\If}} \newcommand{\sequencej}[1]{\left\{ {#1}_j \right\}_{j\in\If}} \newcommand{\basphi}{\varphi} \newcommand{\baspsi}{\psi} \newcommand{\refphi}{\tilde\basphi} \newcommand{\sinL}[1]{\sin\left((#1+1)\pi\frac{x}{L}\right)} \newcommand{\xno}[1]{x_{#1}} \newcommand{\yno}[1]{y_{#1}} \newcommand{\dX}{\, \mathrm{d}X} \newcommand{\dx}{\, \mathrm{d}x} \newcommand{\ds}{\, \mathrm{d}s} \newcommand{\Real}{\mathbb{R}} $$

 

 

 

Bibliography

  1. H. P. Langtangen. Approximation of functions, http://tinyurl.com/k3sdbuv/pub/approx.
  2. M. G. Larson and F. Bengzon. The Finite Element Method: Theory, Implementation, and Applications, Texts in Computational Science and Engineering, Springer, 2013.
  3. D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, third edition, Cambridge University Press, 2007.
  4. S. Brenner and R. Scott. The Mathematical Theory of Finite Element Methods, third edition, Springer, 2007.
  5. C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover, 2009.
  6. K. Eriksson, D. Estep, P. Hansbo and C. Johnson. Computational Differential Equations, second edition, Cambridge University Press, 1996.
  7. A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations, Springer, 1994.