Discretization errors | GG-Cell | LSQ-basic | |
---|---|---|---|
Face midpoint value approximation | face AB | \( \frac{1}{72}\left(-{\left(-2x+y\right)}^2\cos xy-\sin x-4\sin y+4\sin xy\right){dx}^2+O\left({dx}^3\right) \) | – |
face BC | \( \frac{1}{72}\left(-{\left(x-2y\right)}^2\cos xy-4\sin x-\sin y+4\sin xy\right){dx}^2+O\left({dx}^3\right) \) | ||
face AC | \( \frac{1}{72}\left(-{\left(x+y\right)}^2\cos xy-\sin x-\sin y-2\sin xy\right){dx}^2+O\left({dx}^3\right) \) | ||
Gradient reconstruction | error of \( \frac{\partial f}{\partial x} \) | \( \frac{1}{6}\left(\left(2x-y\right)y\cos xy-\sin x+2\sin xy\right) dx+O\left({dx}^2\right) \) | \( \frac{1}{6}\left(\left(2x-y\right)y\cos xy-\sin x+2\sin xy\right) dx+O\left({dx}^2\right) \) |
error of \( \frac{\partial f}{\partial y} \) | \( \frac{1}{6}\left(-x\left(x-2y\right)\cos xy-\mathrm{siny}+2\sin xy\right) dx+O\left({dx}^2\right) \) | \( \frac{1}{6}\left(-x\left(x-2y\right)\cos xy-\mathrm{siny}+2\sin xy\right) dx+O\left({dx}^2\right) \) |