Finite Element Methods on Derivative Least–Square and Semi-Standard Galerkin for Solving Boundary Value Problems

Abstract

In this paper, we derived a Derivative Least–Square Method (DLSM) and Semi-Standard Galerkin Method (SSGM) which are both Finite Element Methods (FEM) for Solving Boundary Value Problems. In the DLSM, the residue was differentiated into a new derivative of the residue R while in the SSGM, we took I, for which D is its basis function. The proposed methods were applied on several boundary value problems and the numerical results obtained are reliable and in good agreement with the exact solutions.