The constructionof quadraticC 1 surfacesfrom B-spline control points is generalized to a wider class of control meshes capable of outlining arbitrary free-form surfaces in space. Irregular meshes with non quadrilateral cells and more or fewer than four cells meeting at a point are allowed so that arbitrary free-form surfaces with or without boundary can be modeled in the same conceptual frame w...

Subdivision surfaces are finding their way into many Computer Aided Design and Animation packages. Popular choices include Loop, Catmull-Clark, Doo-Sabin etc. Subdivision surfaces have many design advantages over traditional use of Non Uniform Rational B-Splines (NURBs). 3D mesh compression has become necessary for transferring and browsing 3D objects over the internet. MPEG-4 has included enco...

In this paper we obtain a range of inverse-type inequalities which are applicable to finite element functions on general classes of meshes, including degenerate meshes obtained by anisotropic refinement. These are obtained for Sobolev norms of positive, zero and negative order. In contrast to classical inverse estimates, negative powers of the minimum mesh diameter are avoided. We give two appl...

in this paper we study the boundary layer problems in which boundary conditions are non-local. here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. by getting help from these conditions, at first the boundary condition is changed from non-local to local. the main aim of this paper is to identify the location of the boundary layer. in ot...

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multiplie...

The problem of the transport of a quantity (heat, matter or momentum) by advection-diiusion is considered for arbitrarily large Peclet number in a two-dimensional domain. In some neighbourhoods of the boundary of the domain, boundary layers may appear for large Peclet number. It is well known that classical nite diierence methods do not yield approximate solutions with a guaranteed accuracy if ...

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for ...

A large-eddy simulation (LES) solver which combines an immersed-boundary technique with a curvilinear structured grid has been developed to study the temporal and spatial dynamics of an incompressible rotor tip-clearance flow. The overall objective of these simulations is to determine the underlying mechanisms for low-pressure fluctuations downstream of the rotor near the endwall. Salient featu...

Zienkiewicz-Zhu's derivative patch recovery technique is analyzed for general quadri-lateral nite elements. Under certain regular conditions on the meshes, the arithmetic mean of the absolute error of the recovered gradient at the nodal points is superconver-gent for the second-order elliptic operators. For rectangular meshes and the Laplacian, the recovered gradient is superconvergent in the m...

We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion équation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H finite volume space. We actually prove...