摘要
For the linear finite element solution to the Poisson equation, we show that supercon- vergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^2-projection from the piecewise constant field △↓UN to the continuous and piecewise linear finite element space gives a better approximation of △↓U in the Hi-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.
For the linear finite element solution to the Poisson equation, we show that supercon- vergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^2-projection from the piecewise constant field △↓UN to the continuous and piecewise linear finite element space gives a better approximation of △↓U in the Hi-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.
基金
supported in part by NSF Grant DMS-0811272
in part by NIH Grant P50GM76516 and R01GM75309
supported in part by NSF Grant DMS 0555831, and DMS 0713743
