Superconvergence for Second Order Triangular Mixed and Standard Finite Elements

JYV ASKYL A 1996 2 Superconvergence for second order triangular mixed and standard nite elements. Abstract In this paper we will prove that both the second order Raviart-Thomas type mixed nite elements and the quadratic standard nite elements on regular and uniform triangular partitions, are superconvergent with respect to Fortin interpolation. This result implies the superconvergence for quadratic standard elements with respect to Lagrange interpolation which was proved by Goodsell e.a..15, 13]. However, our result applies to more triangulations, and allows easy duality estimates resulting in L 2 (()-superconvergence not only for the gradient, but for the scalar function as well. Therefore, we believe that the approach using Fortin interpolation is the more natural, and that it gives more insight into the character of the superconvergence phenomena.