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Boundary Value Problems

Table 11 Numerical results of u at \(t=3\)

From: Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation

m × n

\(\|u^{n}-U^{n}_{h}\|_{1}\)

order

\(\|I_{h}u^{n}-U^{n}_{h}\|_{1}\)

order

\(\|u^{n}-I_{2h}U^{n}_{h}\|_{1}\)

order

32 × 32

24.9412

/

14.8079

/

15.8557

/

64 × 64

10.8178

1.2051

4.1108

1.8488

4.3097

1.8793

128 × 128

5.0430

1.1010

5.9951e − 01

2.7775

6.0899e − 01

2.8230

256 × 256

2.5055

1.0091

9.4431e − 02

2.6664

9.4848e − 02

2.6827

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