To generate 3D mesh TetGen can be easily used. Are there similar functions (or a way to use TetGen) to generate 2d mesh? I know that such functionality can be easily implemented but I would like to use a Mathematica provided function, as I need to experiment with number of nodes in elements and so on. I just want to solve PDE using FEM not really to play around with mesh generation.
You can use TetGen and just make a z axis which is set to 0 (or any other constant). The issue with DelaunayTriangulation (if you want to generate a mesh from a list of points) is that it returns an adjacency list of the edges, which is very hard to turn into the polygons. This thread describes the issue with it.
Adding a z dimention of 0 is simply:
And then to turn the 3d points back into 2d:
Another approach is to use Imtek's package. These deal with both 2 and 3D with interfaces to Shewchuck's triangle and Tetgen respectively.
Imtek can be had from the University of Freiburg. Documentation is extensive.