Discretization errors | GG-Cell | LSQ-basic | |
---|---|---|---|
Face midpoint value approximation | face AB | \( \frac{1}{8}\left(-{x}^2\cos xy-\sin y\right){dx}^2+O\left({dx}^3\right) \) | – |
face BC | \( \frac{1}{8}\left(-{y}^2\cos xy-\sin x\right){dx}^2+O\left({dx}^3\right) \) | ||
face CD | \( \frac{1}{8}\left(-{x}^2\cos xy-\sin y\right){dx}^2+O\left({dx}^3\right) \) | ||
face AD | \( \frac{1}{8}\left(-{y}^2\cos xy-\sin x\right){dx}^2+O\left({dx}^3\right) \) | ||
Gradient reconstruction | error of \( \frac{\partial f}{\partial x} \) | \( \frac{1}{6}\left(\cos x-{y}^3\sin xy\right){dx}^2+O\left({dx}^3\right) \) | \( \frac{1}{6}\left(\cos x-{y}^3\sin xy\right){dx}^2+O\left({dx}^3\right) \) |
error of \( \frac{\partial f}{\partial y} \) | \( \frac{1}{6}\left(\cos y-{x}^3\sin xy\right){dx}^2+O\left({dx}^3\right) \) | \( \frac{1}{6}\left(\cos y-{x}^3\sin xy\right){dx}^2+O\left({dx}^3\right) \) |