A New Approach to Automatic Mesh Generation over Polygonal Domains using all Quadrilaterals of Quintic Order to Decic Order Finite Elements of Complete Lagrange Family (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 have already proposed this automatic quadrilateral mesh generation scheme in our  recent paper[31]. In this scheme  each four node quadrilateral  is converted to higher order quadrilaterals by inserting the midside nodes appropriately. Examples were presented to illustrate the simplicity and efficiency of the new mesh generation method for standard and arbitrary shaped domains for linear to quartic order quadrilaterals.In this paper,we continue our study and generate  meshes of quintic to decic order quadrilaterals for Complete Lagrange family having 24,32,40,49,60 and 72 nodes.They are actually the Serendipity famiy quadrilaterals with appropriate number of interior nodes to incorporate the complete monomial basis of 5th to 10th degree polynomials in bivariates We have appended two  important MATLAB programs which incorporate the mesh generation scheme for the 72-noded  decic order complete Lagrange quadrilateral 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.The typical domains include rectangles,arbitrary oriented rectangles,an equilateral triangle, arbitrary quadrilateral,convex and nonconvex polygons.