The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smooth...

The 3D meshing process begins with the definition of the outer geometry. With a CAD system and a 2d quadrilateral mesh generator, a closed all-quadrilateral mesh is obtained, which is the start point for the process that this communication describes. Once imposed the outer quadrilateral mesh, the connectivity between the inner elements becomes strongly conditioned. Following the guidelines of t...

Stability result is obtained for the approximation of the stationary Stokes problem with nonconforming elements proposed by Douglas et al [1] for the velocity and discontinuous piecewise constants for the pressure on quadrilateral elements. Optimal order H and L error estimates are derived.

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works [9, 8, 4], we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e. the first order accuracy of the velocities in H-norm and the pressure ...

A mesh is said to be dendritic if it contains elements with mid-side (edge) nodes when the predominant element topology has only corner nodes. A dendritic mesh is illustrated in Figure 1 where the predominant element is a four-node quadrilateral, but has also several five-node quadrilateral elements each with one mid-edge node plus four corner nodes. Such meshes arise when an approximately unif...

Classical surface parameterization algorithms often place singularities in order to enhance the quality of the resulting parameter map. Unfortunately, singularities of positive integral index (as the north pole of a sphere) were not handled since they cannot be described with piecewise linear parameter functions on a triangle mesh. Preprocessing is needed to adapt the mesh connectivity. We pres...

A general 2D-hp-adaptive Finite Element FE implementation in Fortran 90 is described. The implementation is based on an abstract data structure, which allows to incorporate the full hp-adaptivity of triangular and quadrilateral nite elements. The h-reenement strategies are based on h2-reenement of quadrilaterals and h4-reenement of triangles. For p-reenement we allow the approximation order to ...

A wide span of steady-state and transient edge plasma processes simulation problems require accurate discretization techniques and can then be treated with Finite Element (FE) and Finite Volume (FV) methods. The software used here to meet these meshing requirements is a 2D finite element grid generator. It allows to produce adaptive unstructured grids taking into consideration the flux surface ...

This paper discusses the problem of subdividing meshes containing tetrahedra, pyramids, prisms or hexahedra into a consistent set of tetrahedra. This problem occurs in computer graphics where meshes with pyramids, prisms or hexahedra must be subdivided into tetrahedra to use efficient algorithms for volume rendering, iso-contouring and particle advection. Another application is for the use of s...