ENO schemes with subcell resolution

The notion is introduced of subcell distribution, which is based on the observation that unlike point values, cell-averages of a discontinuous piecewise-smooth function contain information about the exact location of the discontinuity within the cell. Using this observation an essentially non-oscillatory (ENO) reconstruction technique is designed which is exact for cell averages of discontinuous piecewise-polynomial functions of the appropriate degree. Later on this new reconstruction technique is incorporated into Godunov-type schemes in order to produce a modification of the ENO schemes which prevents the smearing of contact discontinuities.