Table 2 The lower and upper bounds of \(C^{L}(1,\theta )\) for triangles of different shapes
From: Error-constant estimation under the maximum norm for linear Lagrange interpolation
θ | h = 1/32 | h = 1/64 | ||||||
|---|---|---|---|---|---|---|---|---|
d | \(C^{L}_{lb}\) | \(\lambda _{h,B}\) | \(C^{L}_{ub}\) | d | \(C^{L}_{lb}\) | \(\lambda _{h,B}\) | \(C^{L}_{ub}\) | |
π/6 | 9 | 0.31511 | 9.8339 | 0.31904 | 9 | 0.31423 | 9.8925 | 0.31799 |
π/4 | 8 | 0.26777 | 13.517 | 0.27212 | 8 | 0.26753 | 13.574 | 0.27146 |
π/3 | 10 | 0.25182 | 15.412 | 0.25485 | 10 | 0.25209 | 15.457 | 0.25439 |
π/2 | 9 | 0.40432 | 5.5988 | 0.42283 | 9 | 0.40419 | 5.7812 | 0.41596 |
2π/3 | 8 | 0.59964 | 2.3954 | 0.64644 | 8 | 0.60079 | 2.5511 | 0.62618 |
3π/4 | 10 | 0.72146 | 1.5550 | 0.80233 | 10 | 0.72420 | 1.6768 | 0.77235 |
5π/6 | 8 | 0.92197 | 0.93778 | 1.03314 | 8 | 0.92830 | 1.0212 | 0.98968 |