Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian nite elements with straight edges. These elements are allowed to have diameters with diierent asymptotic behaviour in diierent space directions. The case of aane elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered rst. Then, a careful examination of th...

We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements form the cells of a Voronoı̈ diagram, (2) all elements have two opposite 90 angles, (3) all elements are kites, or (4) all angles are at most 120. In each case...

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynam...

We derive a posteriori error estimates for nonconforming discretizations of Poisson's and Stokes' equations. The estimates are residual based and make use of weight factors obtained by a duality argument. Crouzeix-Raviart elements on triangles and rotated bilinear elements are considered. The quadrilateral case involves the introduction of additional local trial functions. We show that their in...

Simple and practical finite-volume schemes for the lattice Boltzmann equation are derived in two and three dimensions through the application of modern finite-volume methods. The schemes use a finite-volume vortex-type formulation based on quadrilateral elements in two dimensions and trilinear hexahedral elements in three dimensions. It is shown that the schemes are applicable to domains with i...

Numerical accuracy and efficiency of several discontinuous high-order methods, including the quadrature based discontinuous Galerkin (QDG), nodal discontinuous Galerkin (NDG), spectral difference (SD) and correction procedure via reconstruction (CPR), for the conservation laws are analyzed and compared on both linear and curved quadrilateral elements. In the CPR formulation, both Lagrange-polyn...

Because of their improved numerical properties, quadrilateral meshes have become a popular representation for finite elements computations and computer animation. In this paper we address the problem of optimally representing quadrilateral meshes as generalized triangle strips (with one swap bit per triangle). This is important because 3D rendering hardware is optimized for rendering triangle m...

Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. ...

The Finite Formulation is an alternative to the widely used Finite Elements or Edge Elements methods and adopts the global variables as a starting point. The Finite Formulation allows one to straightforwardly deduce the set of algebraic equations. This method has been applied to the solution of plane electrostatic problems on the basis of two different topologies of the primal mesh elements: tr...