Post-processing of marginally resolved spectral element data

When derivatives of a spectral element solution are used in a different context, such as visualization or in calculations with a different numerical method, the discontinuity of the derivatives at the element interfaces is a potential problem. Asymptotically, the jumps in the derivatives decay spectrally fast, but it is not always possible or efficient use of computational resources to repeat the spectral element calculations with increased resolution. The usual way of treating the discontinuities is discussed here, however it is not always satisfactory. New methods based on polynomial interpolation across element interfaces and polynomial filtering are suggested, and illustrated by examples.