A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h) for ρ = min(α, 1), when the mesh is distorted O(h) (α > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

In this paper, some patch recovery methods are proposed and analyzed for finite element approximation of elasticity problems using quadrilateral meshes. Under a mild mesh condition, superconvergence results are established for the recovered stress tensors. Consequently, a posteriori error estimators based on the recovered stress tensors are asymptotically exact.

In this paper we utilize affine biquadratic elements and a two-step temporal discretization to develop a finite volume element method for parabolic problems on quadrilateral meshes. The method is proved to have an optimal order convergence rate in L2(0, T ; H1(Ω)) under the ‘asymptotically parallelogram’ mesh assumption. Numerical experiments that corroborate the theoretical analysis are also p...

Starting with a short introduction of the new nonconforming linear quadrilateral P̃1-finite element which has been recently proposed by Park ([13, 14]), we examine in detail the numerical behaviour of this element with special emphasis on the treatment of Dirichlet boundary conditions, efficient matrix assembly, solver aspects and the use as Stokes element in CFD. Furthermore, we compare the num...

We develop stable splitting of the minimal determining sets for the spaces of bivariate C splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer’s method for solving fully nonlinear elliptic PDEs on polygonal domains.

The finite displacement formulation of a quadrilateral element containing an embedded displacement discontinuity is presented. The formulation is based on the kinematically optimal technique, and some known defects of this technique are addressed. Lagrange multipliers are adopted to ensure the correct crack closure prior to initiation. Six additional degrees of freedom in each element allow the...

In this paper we present a new unstructured spectral element method for use on triangular and tetrahedral subdomains. The algorithm maintains the accuracy and efficiency of standard quadrilateral/hexahedral spectral element methods but offers greater adaptivity. Standard unstructured meshes can be used and the order of the polynomial expansion can be varied within each triangular/tetrahedral su...

A very important problem in the research of layer structures is modeling cracks on material interface. Due to complex physical and mechanical properties this structure, simulation discontinuities such as interface by traditional finite element methods requires a fine mesh density. Furthermore, smoothing really large amount computational resources. Therefore, extended algorithm which does not re...

The Zienkiewicz–Zhu (ZZ) super-convergent patch recovery technique based on a node neighborhood configuration is used most widely for of the stress field finite element analysis. In this study, an improved ZZ using proposed. procedure in least-squares sense over that consists union elements surrounding under consideration. proposed provides more sampling points and improves performance standard...