I have a two-dimensional mesh generated by triangle (the mesh generator software is not relevant). This software generates a perfect mesh for approximate the solution by piecewice linear functions (P1 mesh).
For example, for the unit square [0,1]x[0,1] in 2D I have a file with the coordinates of its nodes (for example, a mesh with 5 nodes):
1 0.0 0.0 # coordinates of node 1 2 1.0 0.0 # coordinates of node 2 3 1.0 1.0 # coordinates of node 3 4 0.0 1.0 # coordinates of node 4 5 0.5 0.5 # coordinates of node 5
coordinate.dat, which have 4 elements (triangles) whose conectivity is given by the file called
1 1 5 4 # vertices of triangle 1 2 1 2 5 # vertices of triangle 2 3 2 3 5 # vertices of triangle 3 4 5 2 4 # vertices of triangle 4
Now, I need to program problems where the finite element spaces belong to arbitrary polynomial degree, for example, approximate the solution by polynomials of degree 2, 3, etc.
To do this, I need to build a new mesh with new nodes and a new conectivity file with more nodes. An example of the general mesh that I need:
I already know how to calculate the coordinate of all new nodes on each element (it is just a convex combination easy to calculate) but I can't get a easy way to generate the new conectivity file.
I've been thinking for several days how to program a general method for this, but I could not come up with any.
Do you know some method to create meshes P2, P3, ... from a mesh P1? or more precisely, How can I build the new conectivity file?