Spectral element approximations for triangles are not yet as mature as for quadrilaterals. Here we compare different algorithms and show that using an integration rule based on Gauss-points for simplices is of interest. We point out that this can be handled efficiently and allows to recover the convergence rate theoretically expected, even with curved elements.
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Pasquetti, R., Rapetti, F. Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances. J Sci Comput 27, 377–387 (2006). https://doi.org/10.1007/s10915-005-9048-6
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DOI: https://doi.org/10.1007/s10915-005-9048-6