I am looking at the numerical solutions of a problem when using the boundary element method, the exact solution is 0.25
I have 3 errors corresponding to using 20,40 and 80 boundary elements.
I have seen online the order of convergence for discretisation methods uses formula: $$ q = \frac{log(E_1/E_0)}{log(h_1/h_0)} $$ where $q$ is the order of convergence, $E_1 , E_0$ are the errors and $h_1,h_0$ are step sizes. I do not understand what the step sizes would be in this case.
I thought I would look at getting two values for q using error 1 and error 2 (using $h_1 =40, h_0 =20$) but I end up with a negative $q$ which doesn't make sense.