Generalized Galerkin Finite Element Formulation for the Numerical Solutions Of Second Order Nonlinear Boundary Value Problems

Abstract

We use Galerkin finite element method (GFEM) to solve second order linear and nonlinear boundary value problems (BVPs). First we develop FEM formulation for a class of linear and nonlinear BVPs. Then we present convergence analysis of the method. Later, we give the solution of some nonlinear BVPs with Diritchlet, Neumann and Robin boundary conditions. All results are compared with the exact solution and sometimes with the results of the existing method to verify the convergence, stability and consistency of this method. The results are depicted graphically as well as in the tabular form.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 147-159