Adaptive Step-Size Control in Simulation of Diffusive CVD Processes

Table 5

Numerical results for the P-controller for different spatial-steps with 𝐷=0.1 and 𝜆=1.0 as P-value for the controller.

Δ𝑥	Δ𝑡	err=|𝑢num,Δ𝑥,Δ𝑡−𝑢num,fineΔ𝑥,Δ𝑡|	Convergence rate
0.1	0.1	0.077007	3.2531
0.1	0.05	0.016153	4.0077
0.1	0.025	0.0020085	3.9447
0.1	0.0125	0.00026087	1.8276
0.1	0.00625	0.00014699	0
0.05	0.1	0.27873	2.8591
0.05	0.05	0.076833	3.7481
0.05	0.025	0.011437	4.052
0.05	0.0125	0.001379	3.7776
0.05	0.00625	0.00020111	0
0.025	0.1	0.6564	2.4552
0.025	0.05	0.23939	3.2449
0.025	0.025	0.050505	4.008
0.025	0.0125	0.0062781	3.9999
0.025	0.00625	0.00078482	0
0.0125	0.1	1.04	2.1424
0.0125	0.05	0.4711	2.7173
0.0125	0.025	0.14327	3.7251
0.0125	0.0125	0.021668	4.0516
0.0125	0.00625	0.0026133	0
0.00625	0.1	1.2092	1.586
0.00625	0.05	0.80554	2.4179
0.00625	0.025	0.30148	3.2179
0.00625	0.0125	0.064803	4.005
0.00625	0.00625	0.0080726	0