Certain difficulties with the use of quadrilateral or hexahedral finite elements are related to mesh refinement and to element compatibility and quality after refinement. In this paper, special refinement elements are presented that make possible connecting two special elements to one edge of an 8-node quadrilateral element (2D). The main idea in refinement elements is to place some midside nod...

A fully automatic mesher has been developed which is capable of generating both quadrilateral and triangular elements in 2-D and on surfaces using the advancing front algorithm. This allows the formation of meshes which range from being all-quad or nearly all-quad down to all-triangular. In mixed-element meshes, the number of tri elements present is dictated by the maximum allowable level of qu...

This paper presents the development of a 2D solver for inviscid and viscous compressible flows using the spectral difference (SD) method for unstructured grids with mixed elements. A mixed quadrilateral and triangular grid is first refined using one-level h-refinement to generate a quadrilateral grid while keeping the curvature of boundary edges. The SD method designed for quadrilateral meshes ...

In this work, a new method for mesh simpliication and surface reconstruction speciically designed for the needs of CAD/CAM engineering design and analysis is introduced. The method simpliies the original free-form face model by rst constructing restricted curvature deviation regions, generating a boundary conforming nite element quadrilateral mesh of the regions, and then tting a smooth surface...

This paper presents a computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain for finite element analysis. The proposed method creates a well-shaped single-layered, multi-layered, or partially multi-layered quadrilateral mesh. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analysis of a ...

In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method. Mathematics Subject C...

The flux reconstruction (FR) approach to high-order methods has proved to be a promising alternative to traditional discontinuous Galerkin (DG) schemes since they facilitate the adoption of explicit time-stepping methods suitable for parallel architectures like GPUs. The FR approach provides a parameterized family of schemes through which various classical schemes like nodal-DG and spectral dif...