Finite Element Method: A Galerkin Approach

The finite element method is a means of formulating an approximate solution to a given equation in terms of known coordinate functions and unknown parameters. This approximate solution may be used in conjunction with a number of techniques to determine the unknown parameters. Rayleigh-Ritz and virtual work procedures have commonly been used. The application of a Glaerkin method is analyzed and a class of problems defined for which convergence is ensured. This class is wider than that to which the Rayleigh-Ritz procedure is applicable. Natural boundary conditions are defined and it is shown that the Galerkin procedure often does not require the approximating functions to satisfy these conditions. Interelement continuity requiremetns that are sufficient to ensure convergence are also presented.