Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be used to form a posteriori error estimators for accessing actual errors of the Petrov-Galerkin finite element solutions. Numerical examples are also provided to illustrate the theoretical results obtained in this paper.     

Slow Passage through a Saddle-Center Bifurcation

Received September 24, 1998; accepted August 9, 1999     

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

The use of an adjoint technique for goal‐based error estimation described by Hartit et al. (Int. J. Numer. Meth. Fluids 2005; 47 :1069–1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thin‐film approximation of the flow of a non‐Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one‐dimensional case. The application of a goal‐based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated. Copyright © 2010 John Wiley & Sons, Ltd.     

高次Wilson元的收敛性分析

给出了Poisson方程的非协调高次Wilson有限元方法的收敛性分析,并得到最优误差估计,同时通过数值算例验证了理论分析的正确性.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

Free Subgroups of Groups with Nontrivial Floyd Boundary

Abstract

We prove that when a countable group admits a nontrivial Floyd-type boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding well-known results for hyperbolic groups and groups with infinitely many ends. It also shows that no finitely generated amenable group admits a nontrivial boundary of this type. This improves on a theorem by Floyd (Floyd, W. J. (1980). Group completions and limit sets of Kleinian groups. Invent. Math. 57: 205–218) as well as giving an elementary proof of a conjecture stated in that same paper. We also show that if the Floyd boundary of a finitely generated group is nontrivial, then it is a boundary in the sense of Furstenberg and the group acts on it as a convergence group.     

Film-thickness Error Analysis of Optical Disk Systems

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｒｅｃｅｎｔｌｙｏｐｔｉｃａｌｄｉｓｋｓａｂｌｅｔｏｓｔｏｒｅａｌａｒｇｅｑｕａｎｔｉｔｙｏｆｉｎｆｏｒｍａｔｉｏｎｈａｖｅｂｅｅｎｕｓｅｄａｓｃｏｍｐａｃｔｄｉｓｋ (ＣＤ ) ,ｄｉｇｉｔａｌｖｅｒｓａｔｉｌｅｄｉｓｋ(ＤＶＤ) ,ａｎｄｔｈｅｉｒｒｅｃｏｒｄａｂｌｅｏｒｒｅｗｒｉｔａｂｌｅｔｙｐｅｓ(ｓｕｃｈａｓＣＤ Ｒ ,ＣＤ ＲＷ ,ＤＶＤ Ｒ ,ａｎｄＤＶＤ ＲＡＭ ) [1 ] .Ａｎｏｐｔｉｃａｌｄｉｓｋｉｓａｋｉｎｄｏｆｍｕｌｔｉｌａｙｅｒｓｙｓｔｅｍｄｅｐｏｓｉｔｅｄｏｎａ…     

应用英语专业外贸英语函电写作错误分析与建议

国际贸易在经济全球化和全球信息化的过程中得到迅猛的发展，外贸英语函电写作成为国际贸易中必不可少的一项商务活动。本文通过对应用英语专业学生的外贸英语函电习作的分析，探讨了学生函电写作中的常见错误，并提出了相应的建议，以期提高学生的外贸函电写作能力。