https://doi.org/10.26706/IJAEFEA.2.5.20180502

---

Abstract:-

The one of the commonly used methods for solution of partial differential equations is the finite element method. Solution area for the differential equation to be solved in this method; are divided into a number of sub-regions called simple , small , interconnected , finite elements.However , especially in time-dependent partial differential equations, analysis is performed using the moving finite element method instead of the classical finite element method where the solution network changes locally; both faster and more accurate.In this work, moving finite element method is considered. The details of how the original variation on the solution network for he moving finite element method and the monitor function selection, which is an important factor in these changes, are detailed in the two-dimensional case. As application, C ++ based software is implemented and analyzed the transformer’s electric area distribution according to the state of the classical and moving finite elements and the results are compared.

Index Terms:-

Mesh Generation , Finite Element Method, Moving Finite Element

---

REFERENCES

[1] Mehmet Aydın, Beno Kuryel, Gönül Gündüz, Galip Oturanç, 2001,” Diferansiyel Denklemler ve Uygulamaları”,İzmir.

[2] Thomas R. Hughes , 2000, “The Finite Element Method Linear Static and Dynamic Finite Element Method”, Dover Publications, New York

[3] R. Rannacher, 2001, ”Adaptive Galerkin Finite Element Methods for Partial Differential Equations”, Journal of Computational and Applied Mathematics, 128, 205-233.

[4] J.N. Reddy, 1993, An Introduction to Finite Element Method, Second Edition, McGraw-Hill International Editions , New York.

[5] Susan Brenner 2002, “ The Mathematical Theory of Finite Element Method”, RAMEPublishers Verlag Press Berlin.

[6] Weiming Cao, Weizhang Huang, Robert D. Rusell, 1998, ”An r-Adaptive Finite Element Method Based Upon Moving Mesh PDEs” ,Journal of Computational Physiscs, 149, pp: 221-244.

[7] Weiming Cao, Weizhang Huang, Robert D. Rusell, 1998, ”An r-Adaptive Finite Element Method Based Upon Moving Mesh PDEs” ,Journal of Computational Physiscs, 149, pp: 221-244.

[8] Weiming Cao, Weizhang Huang, Robert D. Rusell,1994, “A Study Of Monitor Functions For Two-Dıemensional Adaptive Mesh Generation”, SIAM J. SCI.Computer, Vol:20 No: 6, pp: 1978-1994.

[9] Miller K, Miller R.N, 1981, “Moving Finite Elements:Part 1”, SIAM J.Numer Anal 18: 1019-1052.

[10] Jimack P,1988 a, “High order moving finite elements II”, Report number AM-88-03 School of Mahtematics,University of Bristol,U.K

[11] Johnson, I.W,Wathen, A., Baines, M.J (1988) Moving Finite Elements for Evolutionary Problems(II) Applications. J.Comput. PHYS. 79 pp 270-297.

[12] Carlson, N.,Miller, K. (1986) Gradient Weighted Moving finite Elements in Two Dimensions. PAM-347. Center for Pure and Applied Mathematics, University of California,Berkley,USA.

---

To view full paper, Download here

---