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Theory and Modern Applications

Table 2 Approximate error of the stabilized finite scheme for test 2 with \(\mathbf{K}=0.1 \mathbb{I}\)

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

0.0161660000

0.1895230

0.05247790

0.048723100

1.4312000

0.0205940000

1/8

0.0040720000

0.0944033

0.01628890

0.011688300

0.7203930

0.0054969900

1/16

0.0010201200

0.0471172

0.00525163

0.002889210

0.3606690

0.0014169300

1/32

0.0002548480

0.0235401

0.00174311

0.000721144

0.1804010

0.0003594990

1/64

6.37027e–005

0.0117660

0.00059351

0.000180326

0.0902083

9.05304e–005