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Table 3 The errors for different time step Δt and space step h at \(t=1\) and convergence orders

From: A B-spline finite element method for solving a class of nonlinear parabolic equations modeling epitaxial thin-film growth with variable coefficient

t,h) \(\|u-u_{h}\|\) rate \(\|u-u_{h}\|_{1}\) rate \(\|u-u_{h}\|_{2} \) rate
(1/100,1/10) \(1.8855e^{-4}\)   \(7.0332e^{-3}\)   \(4.3020e^{-1}\)  
(1/400,1/20) \(1.0720e^{-5}\) 4.1366 \(8.1374e^{-4}\) 3.1116 \(1.0389e^{-1}\) 2.0500
(1/1600,1/40) \(6.5496e^{-7}\) 4.0327 9.9694−5 3.0290 \(2.5745e^{-2}\) 2.0127
(1/6400,1/80) \(4.0685e^{-8}\) 4.0088 \(1.2399e^{-5}\) 3.0073 \(6.4221e^{-3}\) 2.0032