Parametric Interpolation To Scattered Data [QA281. A995 2008 f rb].

Dua skema interpolasi berparameter yang mengandungi interpolasi global untuk data tersebar am dan interpolasi pengekalan-kepositifan setempat data tersebar positif dibincangkan. Two schemes of parametric interpolation consisting of a global scheme to interpolate general scattered data and a local positivity-preserving scheme to interpolate positive scattered data are described

Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates

In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a smooth, compact embedded submanifold \M\subset \R^d. For restricted kernels having finite smoothness, we provide a complete characterization of the native space on \M. After this and some preliminary setup, we present Sobolev-type error estimates for the interpolation problem. Numerical results verifying the theory are also presented for a one-dimensional curve embedded in $\R^3$ and a two-dimensional torus

High-order finite elements on pyramids: approximation spaces, unisolvency and exactness

We present a family of high-order finite element approximation spaces on a pyramid, and associated unisolvent degrees of freedom. These spaces consist of rational basis functions. We establish conforming, exactness and polynomial approximation properties.Comment: 37 pages, 3 figures. This work was originally in one paper, then split into two; it has now been recombined into one paper, with substantial changes from both of its previous form

Justification of the Cauchy-Born approximation of elastodynamics

We present sharp convergence results for the Cauchy-Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time interval

Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy-Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.Comment: new version with only minor change