Manuscript En06-A@1 · En06-A.tex · section · e04c9892

Increasing stencils: the geometric escape

Increasing stencils: the geometric escape · lines 1016–1037

En06-A@1#eq:family

Choose sequences

ε_{n} ↓ 0, δ_{n} ↓ 0, L_{n} \geq 4 D / δ_{n},

and corresponding stencils $S_{n}$ . Set

h_{n} = ε_{n} / L_{n}, Λ_{n} = h_{n} Z^{D}, Δ t_{n} = ε_{n} / c, P_{n} = conv {s / L_{n} : s \in S_{n}} .

The word metric is

d_{n} (h_{n} z, h_{n} z^{'}) = d_{S_{n}} (z, z^{'}),

and the combinatorial block radius is $r = 1$ .

Displayed formulas in this passage

En06-A@1#eq:family · line 1025
$h_{n} = ε_{n} / L_{n}, Λ_{n} = h_{n} Z^{D}, Δ t_{n} = ε_{n} / c, P_{n} = conv {s / L_{n} : s \in S_{n}} .$
unlabeled · line 1019
$ε_{n} ↓ 0, δ_{n} ↓ 0, L_{n} \geq 4 D / δ_{n},$
unlabeled · line 1033
$d_{n} (h_{n} z, h_{n} z^{'}) = d_{S_{n}} (z, z^{'}),$