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Theory and Modern Applications

Table 1 The errors for different 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

(1/8000,1/10)

\(2.0642e^{-4}\)

 

\(7.0170e^{-3}\)

 

\(4.3022e^{-1}\)

 

(1/8000,1/20)

\(1.4750e^{-5}\)

4.1349

\(8.1325e^{-4}\)

3.1091

\(1.0389e^{-1}\)

2.0500

(1/8000,1/40)

\(7.1398e^{-7}\)

4.0406

\(9.9680e^{-5}\)

3.0283

\(2.5745e^{-2}\)

2.0127

(1/8000,1/80)

\(4.1614e^{-8}\)

4.1614

\(1.2399e^{-5}\)

3.0071

\(6.4221e^{-3}\)

2.0032