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Theory and Modern Applications

Table 4 Approximate error of the stabilized finite element scheme for test 2 with \(\mathbf{K}=0.001 \mathbb{I}\)

From: Stabilized finite element method for the stationary mixed Stokes–Darcy problem

h

\(\|\mathbf{u}_{f}^{h}-\mathbf{u}_{f}\|_{0,\Omega _{f}}\)

\(\|\mathbf{u}_{f}^{h}-\mathbf{u}_{f}\|_{1,\Omega _{f}}\)

\(\|p^{h}-p\|_{0,\Omega _{f}}\)

\(\|\phi ^{h}-\phi \|_{0,\Omega _{p}}\)

\(\|\phi ^{h}-\phi \|_{1,\Omega _{p}}\)

\(\|\mathbf{u}^{h}_{p}-\mathbf{u}_{p}\|_{0,\Omega _{p}}\)

1/4

0.016845100

0.1902420

0.12546000

4.5981200

143.695

0.022608400

1/8

0.005788180

0.0964517

0.05396490

1.1318200

72.1796

0.006306740

1/16

0.002560890

0.0488275

0.01943480

0.2813460

36.0814

0.001683910

1/32

0.001052120

0.0242530

0.00616251

0.0705812

18.0412

0.000422170

1/64

0.000358495

0.0119415

0.00191977

0.0177721

9.02091

0.000101925