Midterm study guide

For the midterm you should be able to:

Finite differences (FD)
- write down basic FD approximations to differential operators, equations, and boundary/initial conditions
- determine the order of approximation (and prove)
- judge whether an initial-value problem is stable (or for what parameters it is stable)
- understand how to implement FD on a computer
Finite elements (FE)
- fomulate a (boundary-value problem for a) PDE in a weak form
- formulate a FE problem, finite element space (piecewise linear functions)
- write down the stiffness matrix in simple cases
- understand how to implement FE on a computer
Spectral methods (SM)
- formulate a spectral method for a given PDE
- write down the stiffness matrix in simple cases
- understand how to implement SM on a computer
Multigrid
- understand the idea of multigrid: smoothing, restriction, prolongation
- understand how to choose the $A_h$ operators on a coarse grid from a fine grid
- formulate the smoothing property in terms of high/low frequences



In [1]:

    
from IPython.core.display import HTML
def css_styling():
    styles = open("./styles/alex.css", "r").read()
    return HTML(styles)
css_styling()









    Out[1]:

Fast PDE/IE course, Skoltech, Spring 2015

Midterm study guide