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Boundary Value Problems

Table 9 Numerical results of u at \(t=1\)

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

29.0467

/

12.6079

/

13.3593

/

64 × 64

13.7423

1.0797

4.1904

1.5891

4.3447

1.6205

128 × 128

6.6382

1.0497

1.2041

1.7990

1.2251

1.8262

256 × 256

3.2728

1.0202

2.5485e − 01

2.2402

2.5658e − 01

2.2555

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