EOC and Error to Runtime Ratio

To determine the numerical order of convergence (EOC) we have applied our method to a problem for which we can construct an exact solution. The first two pictures show the EOC of our method with linear (ESC1-IRK) and with quadratic ansatz functions (ESC2-IRK) respectivly. We also compared our method with other method in respect to their error to runtime ratio. Our method reaches a fixed error in up to one procent of the time required by other often used methods.