A New Approach to Automatic Mesh Generation over Polygonal Domains with Linear, Quadratic,Cubic and Quartic Order Quadrilaterals of Serendipity, Lagrange and Complete Lagrange Finite Elements (International Journal of Engineering and Computer Science, 2020)
This paper presents a novel mesh generation scheme of all quadrilateral elements over  a linear polygonal domain. We first decompose the  linear polygon into simple sub regions in the shape of quadrilaterals. These simple regions are then quadrangulated to generate first into a fine mesh of four node quadrilateral elements using bilinear transformations.We propose then an automatic quadrilateral conversion scheme. Each four node quadrilateral  is converted to an 8-node,9-node,12-node ,16-node,17-node and 25-noded quadrilaterals by inserting the midside nodes appropriately. Examples are presented to illustrate the simplicity and efficiency of the new mesh generation method for standard and arbitrary shaped domains. We have appended two  important MATLAB programs which incorporate the mesh generation scheme for the 17-noded complete Lagrange elements developed in this paper.Other MATLAB programs can be coded on similar lines. These programs provide valuable  output on the nodal coordinates ,element connectivity  and graphic display of the all quadrilateral meshes for application to finite element analysis.