✦ LIBER ✦

A convergence rate theorem for finite difference approximations to delta functions

✍ Scribed by John D. Towers

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 162 KB
Volume: 227
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2008.03.019

No coin nor oath required. For personal study only.

✦ Synopsis

We prove a rate of convergence theorem for approximations to certain integrals over codimension one manifolds in R n . The type of manifold involved here is defined by the zero level set of a smooth mapping u : R n 7 !R. Our approximations are based on the two finite difference methods for discretizing delta functions presented in . We included a convergence proof in that paper, but only proved rates of convergence in some greatly simplified situations. Numerical experiments indicated that our two methods were at least first and second order accurate, respectively. In this note we prove those empirical convergence rates for the two algorithms under fairly general hypotheses.

📜 SIMILAR VOLUMES

A rate of convergence for monotone finit

A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs

✍ Luis A. Caffarelli; Panagiotis E. Souganidis 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB

Probability methods for the convergence

Probability methods for the convergence of finite difference approximations to partial differential equations

✍ Harold J Kushner; Chen-Fu Yu 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 959 KB

A convergence rate analysis for markov f

A convergence rate analysis for markov finite approximations to a class of Frobenius-Perron operators

✍ Jiu Ding; Tien Yien Li 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 482 KB

A Weak Convergence Theorem for Functiona

A Weak Convergence Theorem for Functionals of Sums of Martingale Differences

✍ Z. Rychlik; I. Szyszkowski 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 195 KB

For each n, let ( S n k ) , 1 S k s k,, be a mean zero square -integrable martingale adapted to increasing a-fields ($nk), O s k s h n , and let ( b n k ) , OSkaE,, be a system of random variables such that bno=O -=bnl-=... -= bnkn= 1 and such that bnk is Snn,k-l measurable for each k. We present su

A convergence theorem for ritz approxima

A convergence theorem for ritz approximations of eigenvalues with application to CI-calculations

✍ A. Bongers 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 469 KB

For self-adjoint operators having isolated cisenvalucs of finite multiplicity in the lower part of their spectrum NC prove a convergence theorem for Rayleigh-Ritz approximations under weak complctencss assumptions on the basis functions. The result is applied to CLcalculations for molecules.

Convergence analysis of finite differenc

Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem

✍ G. Beckett; J.A. Mackenzie 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 206 KB

We derive ε-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, ε is the small parameter multiplying the highest derivative term. The grid is suggested by the equidistribut