A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations

We describe an adaptive mesh refinement finite element method-of-lines procedure for solving one-dimensional parabolic partial differential equations. Solutions are calculated using Galerkin's method with a piecewise hierarchical polynomial basis in space and singly implicit Runge-Kutta (SIRK) methods in time. A modified SIRK formulation eliminates a linear systems solution that is required by the traditional SIRK formulation and leads to a new reduced-order interpolation formula. Stability and temporal error estimation techniques allow acceptance of approximate solutions at intermediate stages, yielding increased efficiency when solving partial differential equations. A priori energy estimates of the local discretization error are obtained for a nonlinear scalar problem. A posteriori estimates of local spatial discretization errors, obtained by order variation, are used with the a priori error estimates to control the adaptive mesh refinement strategy. Computational results suggest convergence of the a posteriori error estimate to the exact discretization error and verify the utility of the adaptive technique.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-90-0194; the U.S. Army Research Office under Contract Number DAAL 03-91-G-0215; by the National Science Foundation under Grant Number CDA-8805910; and by a grant from the Committee on Research, Tulane University.     

The thermal properties of some metal complexes of diethyldithiocarbamic acid

The cobalt(II), cadmium(II), copper(II), mercury(II), nickel(II) and zinc(II) complexes of diethyldithiocarbamic acid were prepared and investigated by TG, DSC thin-layer chromatography and gas-liquid chromatography. Heats of fusion were determined.Permission to publish this paper has been given by the Government Chemist, Ministry of Technology.     

A conventional proof of Kerr's Theorem

A proof of Kerr's Theorem for generating geodesic and shearfree null congruences in Minkowski space is given in the Newman-Penrose null tetrad formalism.Supported in part by NSF Grant GP-43844-X.     

Carbonate formation and decomposition on atomic oxygen precovered Au(111)

Experimental results supported by density functional theory calculations show carbonate formation and reaction on atomic oxygen precovered Au(111). Oxygen mixing is observed in temperature-programmed desorption measurements when a Au(111) precovered with 16O is exposed to isotopically labeled CO2 (C18O2). The presence of 16O18O is attributed to surface carbonate formation and decomposition at surface temperatures ranging from 77-400 K and initial oxygen coverages ranging from 0.18-2.1 ML. A reaction probability on the order of 10(-4) and an activation energy of -0.15+/- 0.08 eV are estimated for this reaction.     

A one-pot synthesis of unsymmetrical bis-styrylbenzenes

An efficient and widely applicable one-pot synthesis of unsymmetrical (E,E)-bis-styrylbenzenes using successive Heck and Horner-Wadsworth-Emmons reactions is described.     

Quantitative Acoustic Microscopy for Determination of Properties of Hard Coatings

 For quantitative assessment of the properties of hard coatings there is an increasing demand for testing methods with high reliability of the test results, especially concerning the independence of the method and the comparability between different laboratories. This includes the knowledge about all the factors which influence the test procedure itself, determination of best testing conditions, testing of these conditions in round-robins to get a view of the comparability of results, and formulation of guidelines for standardization. In a European project several test methods for hard coatings on steel were investigated for this purpose and the elastic moduli of the coating and coating thickness were determined non-destructively by means of quantitative acoustic microscopy. This method and the instruments available had not yet been certified in the fields of coatings simply owing to the absence of standardised signal processing, followed by the determination of sound velocities and materials parameter extraction. For this purpose four laboratories carried out investigations and measurements on reference samples and on two types of hard coatings (titanium nitride and C-doped chromium) on M2 tool steel.     

Second-order finite element approximations and a posteriori error estimation for two-dimensional parabolic systems

Summary We discuss an adaptive local refinement finite element method of lines for solving vector systems of parabolic partial differential equations on two-dimensional rectangular regions. The partial differential system is discretized in space using a Galerkin approach with piecewise eight-node serendipity functions. An a posteriori estimate of the spatial discretization error of the finite element solution is obtained using piecewise fifth degree polynomials that vanish on the edges of the rectangular elements of a grid. Ordinary differential equations for the finite element solution and error estimate are integrated in time using software for stiff differential systems. The error estimate is used to control a local spatial mesh refinement procedure in an attempt to keep a global measure of the error within prescribed limits. Examples appraising the accuracy of the solution and error estimate and the computational efficiency of the procedure relative to one using bilinear finite elements are presented.Dedicated to Prof. Ivo Babuka on the occasion of his 60th birthdayThis research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0156 and the U.S. Army Research Office under Contract Number DAAL 03-86-K-0112