This paper describes and demonstrates a process for adaptive refinement of quadrilateral curved shell meshes using error estimates from MSC.Nastran. The meshes have been generated originally using Unigraphics'(UG) Scenario application. Although refinement procedures for finite element meshes have been in use for many years, automated procedures have most generally been developed for triangular ...

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve this for any mesh composed of simplex elements, and deal.II contains a serial algorithm to construct a consistent orientation of any quadrilateral mesh of an ...

Occasionally one may be confronted by a hexahedral or quadrilateral mesh containing doublets, two faces sharing two edges. In this case, no amount of smoothing will produce a mesh with agreeable element quality: In the planar case, one of these two faces will always have an angle of at least 180 degrees between the two edges. We describe a robust scheme for refining a hexahedral or quadrilatera...

We study a new mixed finite element of lowest order for general quadrilateral grids which gives optimal order error in the H(div)-norm. This new element is designed so that the H(div)-projection Ph satisfiesr Ph = Phdiv. A rigorous optimal order error estimate is carried out by proving a modified version of the Bramble–Hilbert lemma for vector variables. We show that a local H(div)-projection r...

This paper presents a convergence analysis of the multi point flux approximation control volume method, MPFA, in two space dimensions. The MPFA version discussed here is the so–called O–method on general quadrilateral grids. The discretization is based on local mappings onto a reference square. The key ingredient in the analysis is an equivalence between the MPFA method and a mixed finite eleme...

A two-dimensional unstructured elliptic smoothing method is described where the Winslow equations are discretized using a finite volume approach. Virtual control volumes for each node are constructed with element shapes that are nearly ideal. Green-Gauss theorem is used to formulate gradients over an element or a collection of elements for a node, which ultimately leads to a coupled non-linear ...

We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous Pr−1-elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition u...

In this paper we study the convergence of adaptive finite element methods for the general non-affine equivalent quadrilateral and hexahedral elements on 1-irregular meshes with hanging nodes. Based on several basic ingredients, such as quasi-orthogonality, estimator reduction and Döfler marking strategy, convergence of the adaptive finite element methods for the general second-order elliptic pa...

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and...

The use of finite element (FE) analysis in the simulation of physical phenomena over the human body has necessitated the construction of meshes from images. Despite the availability of several tools for generating meshes for FE-based applications, most cannot deal directly with the raw pixel-wise representation of image data. Additionally, some are optimized for the construction of much simpler...