A method for solving an equation by approximating continuous quantities as a set of quantities at discrete points, often regularly spaced into a so-called grid or mesh. Because finite element methods can be adapted to problems of great complexity and unusual geometry, they are an extremely powerful tool in the solution of important problems in heat transfer, fluid mechanics, and mechanical systems. Furthermore, the availability of fast and inexpensive computers allows problems which are intractable using analytic or mechanical methods to be solved in a straightforward manner using finite element methods.

REFERENCES:

Akin, J. E. Finite Elements for Analysis and Design. San Diego: Academic Press, 1994.

Brenner, S. C. and Scott, L. R. The Mathematical Theory of Finite Element Methods. New York: Springer-Verlag, 1994.

Gallagher, R. H. Finite Element Analysis: Fundamentals. Englewood Cliffs, NJ: Prentice-Hall, 1975.

Kwon, Y. W. and Bang, H. The Finite Element Method Using MATLAB. Boca Raton, FL: CRC Press, 1996.

Kythe, P. K.; Puri, P.; and Schäferkotter, M. R. "Finite Difference Methods." Ch. 10 in Partial Differential Equations and Mathematica. Boca Raton, FL: CRC Press, pp. 321-349, 1997.

Özisik, M. N. Finite Difference Methods in Heat Transfer. Boca Raton, FL: CRC Press, 1994.

Reddy, J. N. and Gartling, D. K. The Finite Element Method in Heat Transfer and Fluid Dynamics. Boca Raton, FL: CRC Press, 1994.

White, R. E. An Introduction to the Finite Element Method with Applications to Nonlinear Problems. New York: Wiley, 1985.