Spectral method(谱方法)
连续变换
$\bar{u}j$, 计算点值$u{j+\frac{1}{2}}^-$.
间断变换
ENO: adaptively choose stencil to reduce oscillation. Given the cell average Find a $k$-th order accurate estimates for the values of $u(x)$ at the cell boundaries. Particularly the basis of this approximation is formed by polynomials of degree at most $k − 1$.
1st order
$u_{j+\frac{1}{2}}^- = \bar{u}_j$: 直接用平均值代替点值。
2nd order
在stencil$[\bar{u}{j-1},\bar{u}{j}]$或$[\bar{u}{j},\bar{u}{j+1}]$上计算 $u_{j+\frac{1}{2}}^-$: [u^-_{j+\frac{1}{2}} = ]
WENO推导
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