Function, Derivative and High-Order Derivatives Recovery Methods Using the Local Symmetry Projection

Superconvergent Recovery of Rectangular Edge Finite Element Approximation by Local Symmetry Projection

“…Let t 12 = t 43 = [1 0], t 23 = t 14 = [0 1] be the unit vector along the four edges of K O j . Now we apply the local symmetry recovery method [32] to edge elements as follows: let v h ∈ V h be a vector function. We find…”

“…It is well-known that the symmetry plays an important role in deriving superconvergence results. For example, Yi et al [32] have used the symmetry property to propose a superconvergent recovery method, and obtained the superconvergent recovered quantity for the standard finite element solution by the recovery method. Huang et al [14][15][16] also show the importance of symmetry and obtain the superconvergent recovered quantity.…”

“…Huang et al [14][15][16] also show the importance of symmetry and obtain the superconvergent recovered quantity. The goal of this paper is to extend the local symmetry projection method [32] to the rectangular edge finite element solution for Maxwell's equations. We obtain the superconvergence of the recovered edge finite element solution at the interior vertex under the discrete l 2 norm.…”