A robust direct variational approach for generation of quadrangular and triangular grids on planar domains

We consider the problem of the quadrangular and triangular grid generation. The algorithm proposed for the solution of this problem is based on a generalization of the so called variational method. In particular, this generalization takes into account a combination of length and area functionals for a given triangular grid related to the quadrangular grid under consideration. As a consequence of this generalization high quality triangular grids of a given domain are obtained in a straightforward way from the quadrangular grids computed by this algorithm. We test the proposed algorithm on standard numerical examples.