Mesh adaptation methods can improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving quadrilateral and hexahedral meshes, local modifications which maintain the original element type are desired. For triangle and tetrahedral meshes, effective refinement and coarsening methods that satisfy these criteria are available. Refinement methods...

In many FEM applications, hexahedral meshes are necessary to get the best results. However the automatic generation of an hexahedral mesh from an arbitrary 3D geometry still remains a challenge. In this paper, we propose an extension of the reliable Whisker Weaving algorithm [6]. The Whisker Weaving algorithm starts from a pre-meshed quadrilateral surface, it generates hexahedral meshes for a l...

A new low order membrane nite element is presented. The element formulation is based on the variational principle of Hughes and Brezzi employing an independent rotation eld. In the present work nonconforming interpolation is used for the drill rotation eld. Both triangular and quadrilateral elements are considered. Combined with the Reissner-Mindlin plate bending element of O~ nate, Zarate and ...

An analysis of the finite element heterogeneous multiscale method for a class of quasilinear elliptic homogenization problems of nonmonotone type is proposed. We obtain optimal convergence results for dimension d ≤ 3. Our results, which also take into account the microscale discretization, are valid for both simplicial and quadrilateral finite elements. Optimal a-priori error estimates are obta...

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...

An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no fl...

This paper will describe recent work on the paving algorithm. The paving algorithm is an advancing front meshing method for generating quadrilateral elements on a general three dimensional surface. The work presented in this paper will describe the algorithmic changes to shift the paver from a row by row advancing front to an element by element method. This method modifies the paver to perform ...