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Table 2 The errors for different time step Δt 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
(1/20,1/1000) \(1.3225e^{-3}\)   \(4.7367e^{-3}\)   \(2.9876e^{-2}\)  
(1/40,1/1000) \(3.4476e^{-4}\) 1.9396 \(1.2381e^{-3}\) 1.9357 \(7.7977e^{-3}\) 1.9379
(1/80,1/1000) \(8.6004e^{-5}\) 2.0031 \(3.1124e^{-4}\) 1.9920 \(1.9581e^{-3}\) 1.9936
(1/160,1/1000) \(2.1555e^{-5}\) 1.9964 \(7.8398e^{-5}\) 1.9892 4.9482−4 1.9845