Error Estimate

It can be shown that (Reference)

(10.11)

where C is a constant, p is the order of approximation and h is the (uniform) mesh size, given by

(10.12)

Here, L is the length of the domain and N is the number of elements. Inequality (10.11) shows that as the number of elements ( N ) increases or equivalently the mesh size ( h ) decreases, the norm of the error function decreases, that is, the difference between the exact solution and the FE solution decreases. Thus, FE solution tends to the exact solution when or . The exponent of h in inequality (10.11) denotes the rate of convergence.

Taking the natural logarithm of both sides of the inequality (10.11) and using only the equal sign , we get

(10.13)

Variation of with for various values of p is shown in Fig. 10.1.

Figure 10.1  Variation of error norm with mesh size