The document provides an introduction to the finite element method (FEM) by comparing it to the finite difference method (FDM) in solving a steady state heat conduction problem. It explains key FEM concepts like weighted residuals, interpolation functions, numerical integration using Gauss quadrature, and applying essential boundary conditions. Examples are presented to illustrate the standard FEM procedure of developing element stiffness matrices, applying nodal connectivity, and assembling the global matrix to obtain a numerical solution.

1. An introduction to FEM V.S.S.Srinivas

4. Illustration by example 1 2 3 4 q

5. Solution of FDM

9. FEM-Galerkin Weighted Residuals

13. Concept of Assembly Assembled matrix

16. Interpolation functions from an element point of view

21. Assembly of element matrices nodal connectivity-1D 1 2 3 4 1 2 3 1 2 Local node no. Global node no. 1 - 3, 2 – 4 3 1 - 2, 2 – 3 2 1 - 1, 2 - 2 1 Local to global Element

22. Nodal Connectivity-2D Global node no. Local node no. (i,j) entry in every element conductivity matrix goes to (I,J) entry in global conductivity matrix (i,j)—local node nos, (I,J)—Global node nos. 1 2 3 4 1 5 6 7 8 9 2 3 4 1 2 3 4 1 – 4, 2 – 5,3 – 8, 4 – 7 3 1 – 5, 2 – 6, 3 – 9, 4 – 8 3 2 – 2, 2 – 3,3 – 6,4 – 5, 2 1 – 1,2– 2, 3 – 5, 4 – 4 1 Local to global Element

28. Interpolation functions