Spectral Elements for Transport-Dominated Equations

Daniele Funaro

• 17 april 1997
• 9783540626497

Samenvatting:

The numerical approximation of various PDEs is dealt with in this book, using the spectral element method. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods.



The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.