This paper addresses the recovery of piecewise smooth functions from their discrete data.Reconstruction methods using both pseudo-spectral coefficients andphysical space interpolants have been discussed extensively in theliterature, and it is clear that an a priori knowledge of the jumpdiscontinuity location is essential for any reconstruction techniqueto yield spectrally accurate results with high resolution near thediscontinuities. Hence detection of the jump discontinuities iscritical for all methods. Here we formulate a new localized reconstruction method adapted from themethod developed in Gottlieb and Tadmor (1985) and recently revisited in Tadmor and Tanner (in press). Our procedure incorporates the detection of edges into the reconstruction technique. The methodis robust and highly accurate, yielding spectral accuracy up to a smallneighborhood of the jump discontinuities. Results are shown inone and two dimensions.
