A piecewise-quintic interpolation scheme

In the paper a piecewise quintic polynomial interpolation scheme, based on a four-point stencil and a uniform grid is investigated. The interpolant utilizes four consecutive grid data points and the first derivative estimates at the internal points. Sufficient conditions for the scheme to be positive definite are formulated in terms of the discrete maximum principle. Monotonicity conditions are characterized as admissible variability regions of the respective scheme's parameters. Standard limiter functions for derivative estimates are applied with accuracy gain obtained by relaxing monotonicity constraints near local extrema. Results of numerical tests are presented for regular function interpolation as well as for 1D and 2D advection of standard test profiles. (C) 1996 Academic Press, Inc.