Numerical methods for deterministic partial differential equations (academic year 2024/2025)
Exercises
Tutorials (Jupyter notebooks)
Tutorial (freeFEM)
FreeFEM (freely available on all platforms) is used for the tutorials on the finite element method.
References
- J. D. LAMBERT. Numerical methods for ordinary differential systems: the initial value problem. John Wiley & Sons, 1991.
- E. HAIRER, S. P. NØRSETT, and G. WANNER. Solving ordinary differential equations. I Nonstiff problems, volume 8 of Springer series in computational mathematics. Springer, second revised edition, 1993. DOI: 10.1007/978-3-540-78862-1.
- E. HAIRER and G. WANNER. Solving ordinary differential equations. II Stiff and differential-algebraic problems, volume 14 of Springer series in computational mathematics. Springer, second revised edition, 1996. DOI: 10.1007/978-3-642-05221-7.
- R. J. LEVEQUE. Numerical methods for conservation laws, Lectures in Mathematics. ETH Zürich. Birkhäuser, second edition, 1992. DOI: 10.1007/978-3-0348-8629-1.
- J. C. STRIKWERDA. Finite difference schemes and partial differential equations. SIAM, second edition, 2004. DOI: 10.1137/1.9780898717938.
- J. W. THOMAS. Numerical partial differential equations: finite difference methods, volume 22 of Texts in applied mathematics. Springer, 1995. DOI: 10.1007/978-1-4899-7278-1.
- A. ERN and J.-L. GUERMOND, Theory and practice of finite elements, volume 159 of Applied Mathematical Sciences, Springer, 2004. DOI: 10.1007/978-1-4757-4355-5.
- J. P. BOYD, Chebyshev and Fourier spectral methods, Dover, second revised edition, 2001.
- C. CANUTO, M. Y. HUSSAINI, A. QUARTERONI and T. A. ZANG, Spectral methods. Fundamentals in single domains, Scientific Computation, Springer, 2006. DOI: 10.1007/978-3-540-30726-6.
- J. SHEN, T. TANG and L.-L. WANG, Spectral methods. Algorithms, analysis and applications, volume 41 of Springer Series in Computational Mathematics, Springer, 2011. DOI: 10.1007/978-3-540-71041-7.