This paper presents a new mesh generation method for a  simply connected curved  domain of a planar region which has  curved boundary described by one or more analytical equations. We first decompose this curved domain  into simple sub regions in the shape of curved triangles. These simple regions are then triangulated to generate a fine mesh of   linear triangles in the interior and curved triangles near to the boundary of curved domain.  These simple regions are then triangulated  to create 6-node triangles  by inserting midside nodes to these triangles. Each isolated 6-node triangle is then split into four triangles according to the usual scheme, that is, by using straight lines to join the midside nodes. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex curved  or cracked convex  curved  domains   into all triangles, thus propagating refinements and .The quadrangulation of   graded 3-node linear triangles is done by inserting three midside nodes and a centroidal node.Then each graded triangle is split into three quadrilaterals by using straight lines to join the centroid to the  midside nodes. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain.

We have  approximated the curved boundary arcs by  equivalent parabolic arcs.To preserve the mesh conformity,  a similar procedure is also applied to every triangle of the domain to fully discretize the given curved  domain   into all triangles and quadrilaterals, thus propagating  a  uniform  refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples of a circular disk  and a cracked circular disk  are presented to illustrate the simplicity and efficiency of the new mesh generation method. We have appended the  MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable  output on the nodal coordinates ,element connectivity  and graphic display of the all triangular and quadrilateral mesh for application to finite element analysis.