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Unformatted text preview: 11/17/2010 1 Hamilton Jacobi ENO, WENO, Higher accurate spatial differencing HJ ENO Depending u>0 or <0, we use D or D + to approximate . This is of first order. ENO will still depend on u>0 or <0 (and much more) to decide a polynomial approximation p to then use p x to estimate x . ENO chooses p as an interpolating polynomia x ENO chooses p as an interpolating polynomial but its points of interpolation depend on the function value nearby. 11/17/2010 2 Divided Differences at Grid Points Define i i D = First divided differences: Second divided differences: x D D D i i i = + + 1 1 2 / 1 x D D D i i i = + 2 1 2 / 1 1 2 / 1 2 Third divided differences: x D D D i i i = + + 3 2 2 1 3 2 / 1 Interpolating Polynomial At a given grid point x i , we need to decide the points of interpolation so that the associated interpolating polynomial has the least oscillation....
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