ABSTRACT
The weighted residual methods for constructing approximate solutions of boundary value problems presented in Sections 13.8 to 13.12, have the following serious shortcomings especially when applied to two-or three-dimensional boundary value problems:
1. There is not a systematic procedure available for choosing the functions and (s = 1, 2, ..., S) of the approximate solution (13.54) on whose choice the accuracy of the solution depends. A poor choice of the trial functions (s = 1, 2, ..., S) may produce an ill-conditioned stiffness matrix [S] and thus, it may be difficult to solve the resulting set of linear algebraic equations (13.72).
