The Derivative Ultraconvergence for Quadratic Triangular Finite Elements (Journal of Computational Mathematics, 2021)
This work concerns the ultraconvergence of quadratic finite element approximations of elliptic boundary value problems. A new, discrete least-squares patch recovery technique is proposed to post-process the solution derivatives. Such recovered derivatives are shown to possess ultraconvergence. The keys in the proof are the asymptotic expansion of the bilinear form for the interpolation error and a "localized" symmetry argument. Numerical results are presented to confirm the analysis.