# DOI: 10.26706/IJAEFEA.2.6.20190803

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One of the most commonly used methods in numerical solution of partial differential equations is the finite element method. In the finite element method, the region to be analyzed is divided into sub-sections called solution regions provided that the boundaries of the region are determined. This subdivision method depends on the type of differential equation to be solved. A variety of solution network production techniques are used to subdivide the solution region. By selecting the appropriate method, the solution region is divided into sub-compartments to ensure that the solution is faster and more accurate. The classical finite element method gives accurate results when instant analysis is performed on the solution area. However, in cases where partial differential equations change with time and solution network changes regionally, it is useful to use moving finite element method instead of classical finite element method. The use of a moving finite element method allows analysis to be carried out only in varying regions of the solution network to ensure rapid results. In this study, two dimensional solution network production techniques are mentioned. With the help of the developed program, regional changes on the solution network are explained in detail. As an application, C ++ based software was implemented.

Mesh Generation Methods , Finite Element Method, Moving mesh generation.
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REFERENCES
[1] Mehmet Aydın, Beno Kuryel, Gönül Gündüz, Galip Oturanç, 2001,” Diferansiyel Denklemler ve Uygulamaları”,İzmir.
[2] R. Rannacher, 2001, ”Adaptive Galerkin Finite Element  Methods for Partial Differential Equations”, Journal of Computational and Applied Mathematics, 128, 205-233.
[3] Susan Brenner 2002, “ The Mathematical Theory of Finite Element Method”, Springer Verlag Press Berlin.
[4] Thomas R. Hughes , 2000, “The Finite Element Method  Linear Static and Dynamic Finite Element Method”, Dover Publications, New York
[5] S.H. Lo., 2002, “Finite element mesh generation and adaptive meshing“, Prog. Struct. Analysis Materials, Vol:4, pp:381-399.
[6] Delaunay “B. Sur la sphere vide. Bulletin”, Acade´mie des Sciences URSS. 1934: 793–800
[7] Lawson CL. 1977, “Software for C1 surface interpolation”, Mathematical Software III 161–194.
[8] Baker TJ. 1989, “Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation”, Engineering with Computers 5: 161–175.
[9] Zhu JZ, Zienkiewicz OC, Hinton E & Wu J., 1991, “A New Approach to The Development of Automatic Quadrilateral Mesh Generation”, International Journal for Numerical Methods in Engineering 32: 849–866.
[10] Lee CK., 2000, “Automatic metric advancing front triangulation over curved surfaces”,       Engineering Computations 17(1): 48–74.
[11] Lo SH., 1991, Automatic mesh generation and adaptation by using contours. International Journal for Numerical Methods in Engineering 31: 689–707.
[12] Shephard MS & Georges MK. 1991, “Automatic three-dimensional mesh generation by the finite octree technique”, International Journal for Numerical Methods in Engineering 32: 709–749.
[13] Luiz Vello, Denis Zorin  2001, “4-8 Subdivision”, Computer Aided Geometric Design, vol:18, pp:397-427
[14] Zienkiewicz OC & Phillips DV., 1971, “An automatic mesh generation scheme for plane and curved surfaces isoparametric coordinates”, International Journal for Numerical Methods in Engineering 3: 519–528.
[15] Zhu JZ, Zienkiewicz OC, Hinton E & Wu J., 1991, “A new approach to the development of automatic quadrilateral mesh generation”, International Journal for Numerical Methods in Engineering, 32: 849–866.
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