The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property: max P∈S |(∇u−∇uh)(P)| = O(h2)| lnh|, where ∇uh(P) denotes the average gradient on elements cont...

Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems

In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence b...

Superconvergence of the gradient of finite element solutions

Super convergence of the gradient of approximate solutions to second order elhptic équations is analysed and justified for a large ciass of curved isoparametric quadrilatéral éléments Résumé — On analyse et on justifie la super convergence du gradient des solutions approchées obtenues lors de la résolution d'équations elliptiques du second ordre à Vaide d'éléments isoparamétriques courbes de ty...

Mortar Finite Volume Element Approximations of Second Order Elliptic Problems

Superconvergence Analysis of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients

A new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumption that the oscillating coefficient is periodic, some superconvergence results are derived, which ...