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Boundary Value Problems

Table 10 Numerical results of u at \(t=2\)

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

25.9705

/

14.2278

/

15.2578

/

64 × 64

11.6481

1.1567

4.2769

1.7340

4.4823

1.7672

128 × 128

5.5048

1.0813

9.8468e − 01

2.1188

1.0043

2.1579

256 × 256

2.7120

1.0213

1.4919e − 01

2.7224

1.5014e − 01

2.7419

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