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Theory and Modern Applications

Table 3 Approximate error of the stabilized finite element scheme for test 2 with \(\mathbf{K}=0.01 \mathbb{I} \)

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

0.0165941000

0.1898900

0.09290030

0.46289000

14.34060

0.0215030000

1/8

0.0046533600

0.0948421

0.02580190

0.11471700

7.207800

0.0056623600

1/16

0.0012938400

0.0472456

0.00675441

0.02864350

3.606840

0.0014376000

1/32

0.0003417120

0.0235623

0.00199893

0.00718127

1.804010

0.0003616240

1/64

8.73879e–005

0.0117691

0.00063884

0.00179964

0.902083

9.07503e–005