On strongly regular families of piecewise quasi-uniform triangulations of certain curved plane domains

We construct a strongly regular family of triangulations into straight and curved triangles of a bounded plane domain, the boundary of which consists of a finite number of straight line segments and parabolic arcs. This construction is based on transformations by which the standard isoparametric quadratic element is defined. Further we prove that the proposed triangulations are piecewise quasi-uniform, which produces various superconvergence phenomena when the finite element method is applied.