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ENO schemes with subcell resolution. (English) Zbl 0696.65078
The author gives an idea for constructing an essentially non-oscillatory (ENO) finite difference scheme for problems containing the equation of continuity in the following form: $$u_ t+f(u)_ x=0,\quad u(0,x)=u_ 0(x).$$ The construction is based on the observation that cell averages of a discontinuous piecewise-smooth function contain information about the location of the discontinuity within the cell.
The reader can find a detailed description of the main idea of ENO schemes and its generalization for second and higher order of accuracy. There is an application for Euler equation of gas dynamics. One can find a very interesting numerical example demonstrating the efficiency of proposed scheme.
Reviewer: Gy.Molnárka

##### MSC:
 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 76N15 Gas dynamics, general
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##### References:
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