We briefly review the use of the flow-condition-based interpolation (FCBI) approach for the solution of high Péclet and high Reynolds number flow problems. The basic idea is presented, formulations for quadrilateral and triangular elements are briefly described, and the results of some numerical solutions are given.

In this paper we utilize affine biquadratic elements and a two-step temporal discretization to develop a finite volume element method for parabolic problems on quadrilateral meshes. The method is proved to have an optimal order convergence rate in L2(0, T ; H1(Ω)) under the ‘asymptotically parallelogram’ mesh assumption. Numerical experiments that corroborate the theoretical analysis are also p...

We prove that any PSLG has a conforming quadrilateral mesh with O(n) elements, all angles ≤ 120◦ and all new angles ≥ 60◦ (the complexity and the angle bounds are both sharp). Moreover, all but O(n) of the angles may be taken in a smaller interval, say [89◦, 91◦]. Date: January 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

Quad-morphing is a new technique used for generating quadrilaterals from an existing triangle mesh. Beginning with an initial triangulation, triangles are systematically transformed and combined. An advancing front method is used to determine the order of transformations. An all-quadrilateral mesh containing elements aligned with the area boundaries with few irregular internal nodes can be gene...

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 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...

Solving the wave equation by a C o finite element method requires to mass-lump the term in time of the variational f6rmulation in order to avoid the inversion of a n-diagonal symmetric matrix at each time-step of the algorithm. One can easily get this mass-lumping on quadrilateral meshes by using a h-version of the spectral elements, based on Gauss-Lobatto quadrature formulae but the equivalent...