Introduction

In the last lecture, we studied certain properties of the finite element solution (or FE solution). In particular, we observed that the error between the exact solution and the FE solution is "orthogonal" to the FE solution. Further, we noticed that the FE solution converges to the exact solution, in "energy" norm, from below. Under certain conditions, the FE values at the end-points of the element match with the exact values and the values of the derivatives of the FE solution match with the exact solution at the centre points of the element.

In this lecture, we shall study the variation of some norm of the error with mesh size h .