Lumped mass on triangular unstructured mesh
 

I was wondering what method is used for lumped mass matrices on a triangular mesh. Guass-Lobatto integration rules fail (in my experience) because the jacobian of the transformation from the bi-unit square to the triangle goes to zero on one corner. Therefore, zeros sometimes appear on the diagonals. (I'm not sure if I was clear in that explanation!)

I've been using a row-sum technique because I haven't had much luck with the "special lumping technique". Is that what is usually done?

Thanks!

Petrov,
the transformation as you would describe it would indeed give a singularity when two nodes are projected onto one. Usually, what's done to prevent this is to define the transformation in another way:

A
|\
| \D
|__ \
B C

So D is chosen as the midpoint of the side. The Jacobi in that case behaves well, no singular point. You might read the book by Karniadakis about spectral methods for more on this!

Hope this helps!

Great!

One more question:
Is this the correct generalization to a quadratic element?

(With J in the middle of the triangle)