In this note is presented a method, given nodal values on multi-dimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is “exact” in the sense that given the approximation inherent in the spectral-element method (SEM), no additional error is introduced that exceeds accumulated computer round-off error. The method would be very useful when the SEM provides an adaptive-mesh simulation of a physical quantity whose global Fourier spectrum is of scientific interest, e.g., in dynamically adaptive fluid-dynamics simulations such as [7].
