The intention of these lecture notes is not to duplicate these works, but instead provide an introductory understanding of both theory and application to enable students to use and refer to these texts. Books by Hughes, Bathe, Gresho and Zienkiewicz provide reviews of finite element methods for engineering, while texts by Quarteroni and Valli, Ciarlet, Brezzi and Fortin, and Girault and Raviart provide comprehensive reviews of the mathematical theory underpinning the method. There are a number of excellent texts which detail both the application and theory of finite elements. Since, the method has continued to be the focus of research as well as an important tool for engineers and engineering researchers. The method mentioned in a paper by Courant in 1943 was the focus of intense research in classical engineering disciplines throughout the 1950s-1970s to improve the design and manufacture of everything from bridges to airplanes to cars (for more on the history of finite elements, see J. The finite element method constitutes a key computational tool for engineers to better understand and analyze complex systems.

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