Here the representative cell Z is an semi-infinite domain. The cell
solution u solves the Laplace problem on Z with Dirichlet boundary
condition on the bottom, periodic boundary conditions on the lateral faces,
and it stabilizes exponentially fast in the upper direction. The Robin
constant C we are interested in is precisely the constant to which u
tabilizes.
We use Q

The approximation of the Robin constant C

Cells | Unknowns | Matrix entries | C |
Error (est.) |
---|---|---|---|---|

2 | 36 | 784 | 9.3593619487d-01 | 6.65d-04 |

9 | 156 | 5182 | 9.4073588307d-01 | 1.68d-04 |

21 | 364 | 13146 | 9.4064954874d-01 | 2.41d-06 |

45 | 780 | 28922 | 9.4065210305d-01 | 4.67d-08 |

141 | 2404 | 89142 | 9.4065215007d-01 | 5.49d-10 |

393 | 6573 | 242335 | 9.4065215057d-01 | 7.15d-11 |

Nicolas Neuss, 2017-01-31