Abstract
In this note, we prove that the well known saturation assumption implies that piecewise polynomial interpolation and best approximation in finite element spaces behave in similar fashion. That is, the error in one can be used to estimate the error in the other. We further show that interpolation error can be used as an a posteriori error estimate that is both reliable and efficient.
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Randolph E. Bank was supported by the Alexander von Humboldt Foundation through a Humboldt Research Award, and by the US National Science Foundation through award DMS-1318480.
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Bank, R.E., Yserentant, H. A note on interpolation, best approximation, and the saturation property. Numer. Math. 131, 199–203 (2015). https://doi.org/10.1007/s00211-014-0687-0
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DOI: https://doi.org/10.1007/s00211-014-0687-0