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Boundary Value Problems

Table 8 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

16 × 16

6.1503

/

9.9968e−01

/

1.0411

/

32 × 32

3.0608

1.0067

2.4141e−01

2.0499

2.4919e−01

2.0627

64 × 64

1.5287

1.0015

6.2188e−02

1.9567

6.2752e−02

1.9895

128 × 128

7.6418e−01

1.0003

1.4664e−02

2.0843

1.4697e−02

2.0941

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