Highlights
-
MultiGrid.
This Numerical Method is never going to work for
Hyperbolic Equations.
I have proved it for the 1-D case. But 1-D is embedded in 3-D.
So the result is
valid for 3-D as well.
Nevertheless, there is ongoing research on this topic,
in vain.
-
MultiGrid.
There exist only two flavours for grid refinement
and grid coarsening:
DoubleGrid and
TripleGrid.
-
The distinction between Continuous and Discrete is only gradual,
not essential:
- Least Squares Finite Element Method.
Can only be formulated properly as a
Unification of
Finite Elements and Finite Differences.
Two applications: Ideal Flow in
2-D and
3-D.
The concept of Dual Elements is important with L.S.FEM.
-
Unification of Finite Elements and Finite Differences for
Convection and Diffusion can be accomplished via
Resistor Networks
in 2-D and 3-D.