In this paper the Wilson nonconforming nite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in neg...

This paper introduces a new family of mixed finite elements for solving formulation the biharmonic equations in two and three dimensions. The symmetric stress σ = −∇2u is sought Sobolev space H(divdiv, Ω; $$\mathbb{S}$$ S ) simultaneously with displacement u L2(Ω). By stemming from structure H(div, conforming linear elasticity problems proposed by Hu Zhang (2014), element spaces are constructed...

In this paper, we will investigate the superconvergence of the finite element approximation for quadratic optimal control problem governed by semi-linear elliptic equations. The state and co-state variables are approximated by the piecewise linear functions and the control variable is approximated by the piecewise constant functions. We derive the superconvergence properties for both the contro...

A superconvergence is established in this article for approximate solutions of second order elliptic equations by mixed nite element methods over quadrilaterals. The superconvergence indicates an accuracy of O(h k+2) for the mixed nite element approximation if the Raviart-Thomas or Brezzi-Douglas-Fortin-Marini elements of order k are employed with optimal error estimate of O(h k+1). Numerical e...

We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on Q Ω × 0, T , where Ω is a bounded domain in R d ≤ 4 with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of ourmodel problem inW1,p Ω and Lp Q with 2 ≤ p < ...

The main aim of this paper is to study the error estimates of a nonconforming finite element for general second order problems, in particular, the superconvergence properties under anisotropic meshes. Some extrapolation results on rectangular meshes are also discussed. Finally, numerical results are presented, which coincides with our theoretical analysis perfectly.

In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions, and was developed in [4, 5, 24]. In particular, we show that the superconvergence points for the gradient of the ap...

The finite elements considered in this paper are those of the Serendipity family of curved isoparametric elements. There is given a detailed analysis of a superconvergence phenomenon for the gradient of approximate solutions to second order elliptic boundary value problems. An approach is proposed how to use the superconvergence in practical computations.

We study superconvergence of a semi-discrete finite element scheme for parabolic problem. Our new scheme is based on introducing different approximation of initial condition. First, we give a superconvergence of uh −Rhu, then use a postprocessing to improve the accuracy to higher order.