Superconvergent recovery of gradients of piecewise linear finite element approximations on non-uniform mesh partitions

Abstract

We propose the use of an averaging scheme, which recovers gradients from piecewise linear finite element approximations on the (1 + α˜)—regular triangular elements to gradients of the weak solution of a second-order elliptic boundary value problem in the 2-dimensional space. The recovered gradients, from mid-points of element edges, are superconvergent estimates of the true gradients. This work is an extension of Levine [Levine, IMA J. Numer. Anal. 5, 407 (1985)] and follows some of the ideas therein. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:169–192, 1998