Polynomial Preserving Recovery for High Frequency Wave Propagation

Polynomial preserving recovery (PPR) was first proposed and analyzed in Zhang and Naga in SIAM J Sci Comput 26(4):1192–1213, (2005), with intensive following applications on elliptic problems. In this paper, we generalize the study of PPR to high-frequency wave propagation. Specifically, we establish the supercloseness between finite element solution and its interpolation with explicit dependence on the frequency of wavefield, and then prove the superconvergence of PPR for high-frequency solutions to wave equation based on the supercloseness. We also present several numerical examples of PPR for both lowfrequency and high-frequency wave propagation in order to confirm the theoretical results of superconvergence analysis.