COMPLEX WAVE-NUMBER FOURIER-ANALYSIS OF THE P-VERSION FINITE-ELEMENT METHOD

High-order finite element discretizations of the reduced wave equation have frequency bands where the solutions are harmonic decaying waves. In these so called ''stopping'' bands, the solutions are not purely p ropagating (real wavenumbers) but are attenuated (complex wavenumbers) . In this paper we extend the standard dispersion analysis technique t o include complex wavenumbers. We then use this complex Fourier analys is technique to examine the dispersion and attenuation characteristics of the p-version finite element method. Practical guidelines are repo rted for phase and amplitude accuracy in terms of the spectral order a nd the number of elements per wavelength.