They can be obtained by several techniques. One is to use a more accurate reconstruction of the function from cell averages, such as, for example, a piecewise linear function, and then solve the generalized Riemann problem (see Figure 3.1)
Figure 3.1

Piecewise smooth reconstruction,generalized Riemann problem and high-order extension of the Godunov method.


Weak Solution Scalar Equation Piecewise Linear Function Entropic Solution Monotone Scheme 
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© Birkhäuser Verlag 2009

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