Spurious solutions to vector diffusion and wave field problems

Deterministic problems involving the vector Helmholtz and diffusion equations often exhibit spurious solutions when they are solved using finite-element methods. These nonphysical solutions arise from the same causes as the well-known spurious propagating modes encountered in high-frequency modal analyses. Using postprocessing techniques, these nonphysical solutions are shown to be responsible for inaccuracies in both modal and deterministic solutions throughout the frequency spectrum. Solution accuracy is recovered through use of mixed-order elements that are known to produce spectrally correct finite-element solutions.<>