Evaluation and Visualization Module
The user should first input the parameter μ = [μ1, μ2] such that μ in [1, 100] × [0.15, 0.25] and the timestep nk in [1, 50]. The user should also input a numerical parameter that relates to the desired accuracy of the RB output prediction Npr in [1, 94], Ndu in [1, 60]: the error in our prediction decreases as N increases. In addition, the user may need to input the control inputs, g(t) and h(t), as particular functions of time t.
The code then displays, for the desired parameter value μ = [μ1, μ2], (i) the variation of the field as a function of time, and (ii) the value of the output/quantity of interest. In each case, we also provide a certificate of fidelity that rigorously bounds the error in our RB prediction relative to the highly accurate (and hence very expensive) "truth'' Finite Element solution.