ABSTRACT
Variational formulation of boundary value problems originates from the fact that weighted variational methods provide approximate solutions of such problems. The variational solution of a differential equation reduces the equation to an equivalent variational form. As in the direct finite element analysis, the weak variation formulation of boundary value problems is important to develop the direct Boundary element methods. This approach is derived from the fact that variational methods for finding approximate solutions of boundary value problems, viz., Galerkin, Rayleigh–Ritz, collocation, or other weighted residual methods, are based on the weak variational statements of the boundary value problems. There is some guidance from geometry for such choices; namely, they should satisfy the essential conditions and exhibit the nature of the approximation solutions vis-a-vis the exact solutions.
