# How to analyze the dispersion and dissipation of a certain FEM?

In Finite Difference method or Finite volume textbook. Dispersion/Dissipation can be analyzed by set $u = u_0\exp{\omega t +\mathbf{kx}}$。

However, I cannot find something about this kind of analysis in FEM without convert it to a system of difference equations. And FEM is a little more complex because of there are two function spaces and some time they are not continuous.

Is there example to do it in the framework of FEM? I saw someone used the Eigen value distribution of assembled matrix.

• Looks like a valid question. You may consider putting a bit more effort into it...
– Jan
Aug 6 '18 at 3:49
• Not so easy. In FDM/FVM of 1D problem, the analysis is straightforward. But for FEM, basis of function space need to be specified first. When it comes to Petrov-Galerkin or Discontinuous Galerkin, the only way is to analysis the result matrix. Aug 6 '18 at 14:35
• Sorry, I wanted to say, you could put a bit more effort into the statement of the question. Like an example of the difficulties or references. Or how it works for FVM and what the terms in $u=...$ stand for.
– Jan
Aug 7 '18 at 2:44