Automatic generation of triangular finite element meshes

A method for automatic generation of triangular finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p, such that: MINTπ(T)m(T)⪢c ∀p, p=1,2,… π(T) and h(T) being respectively the diameter of the inscribed circle and the largest edge of a generated triangle T.