We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl,Ω)-compatible finite element basis. The SG formula is applied to the edges of the elements...

We present a novel approach named T-Base for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element – square – can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right trian...

The Lagrange-Galerkin spectral element method for the two-dimensional shallow water equations is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the nonlinearities introduced by the advection operator o...

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 ...

This paper proposes a computational method for fully automated quadrilateral meshing. Unlike previous methods, this new scheme can create a quadrilateral mesh whose directionality is precisely controlled. Given as input: (1) a 2D geometric domain, (2) a desired node spacing distribution as a scalar function deened over the domain, and (3) a desired mesh directionality as a vector eld deened ove...

This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent ...

In this paper, we build on the mesh improvement methods intended for parallel execution with the paving method [1] and introduce topological changes in an existing quadrilateral-only mesh to improve element shape and nodal valence. This discussion is intended to demonstrate the effectiveness of utilizing mesh cleanup operations as a post-processing step to other mesh generation algorithms. The ...

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...

Abstract This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a natural interpolation scheme. The six free parameters are determined using the natural coordinates of the four nodal points (vertices) of the quadri...