The performance of Bank-Weiser's error estimator for quadrilateral finite elements

The error estimator proposed by Bank and Weiser is analyzed in the case of degree p finite element approximations on quadrilateral meshes. It is shown that the scheme is asymptotically exact in the energy norm for regular solutions provided that the degree of approximation is of odd order and the elements are rectangles. Perhaps surprisingly, the hypotheses are necessary, as counterexamples show. © 1994 John Wiley & Sons, Inc.     

Application of bounds for creeping structures subjected to load variations above the shakedown limit

Previous work established upper bounds on work and displacement for creeping structures subjected to load variations above the shakedown limit. The present paper applies these bounds to three structures subjected to constant mechanical loading and to variable imposed strains. The results are in good agreement with those of more detailed calculations.     

Explicit polynomial preserving trace liftings on a triangle

We give an explicit formula for a right inverse of the trace operator from the Sobolev space H¹(T) on a triangle T to the trace space H^1/2(?T) on the boundary. The lifting preserves polynomials in the sense that if the boundary data are piecewise polynomial of degree N, then the lifting is a polynomial of total degree at most N and the lifting is shown to be uniformly stable independently of the polynomial order. Moreover, the same operator is shown to provide a uniformly stable lifting from L₂(?T) to H^1/2(T). Finally, the lifting is used to construct a uniformly bounded right inverse for the normal trace operator from the space H (div; T) to H^–1/2(?T) which also preserves polynomials. Applications to the analysis of high order numerical methods for partial differential equations are indicated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of diastereoisomer impurities in chiral pharmaceutical compounds by capillary electrophoresis

Summary Micellar electrokinetic capillary chromatography (MECC) has been applied to the separation and analysis of diastereoisomer impurities in chiral pharmaceutical compounds. Differences in separation mechanism and selectivity make MECC useful as an alternative method to HPLC for analysis of these synthetic inpurities. Advantages of MECC include high efficiency separations and low consumption of sample and solvents. Water soluble and insoluble pharmaceutical compounds are used to illustrate the separation characteristics and quantitative capabilities of this versatile new analytical technique.     

Local a posteriori error estimators for variational inequalities

Local a posteriori error estimators for finite element approximation of variational inequalities are derived. These are shown to provide upper bounds on the discretization error. Numerical examples are given illustrating the theoretical results. © 1993 John Wiley & Sons, Inc.     

Perception of pitch movement on tonic syllables in British English

A set of intonation contours has been synthesized using "yes" as the carrier word. Discrimination and identification functions have been obtained for these intonation contours. It was found that the stimuli could be classified as "statement," "question," "emphatic statement," and, possibly, "hesitation" and "weak statement." Predicted discrimination functions were calculated from the identification functions, and these were found to be positively correlated with the obtained discrimination functions. This provides evidence for category boundary effects in the perception of intonation.     

An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions

Summary. Additive Schwarz preconditioners are developed for the p-version of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The principal preconditioner consists of decomposing the subspace into local spaces associated with the element interiors supplemented with a wirebasket space associated with the the element interfaces. The wirebasket correction involves inverting a diagonal matrix. If exact solvers are used on the element interiors then theoretical analysis shows that growth of the condition number of the preconditioned system is bounded by for an open surface and for a closed surface. A modified form of the preconditioner only requires the inversion of a diagonal matrix but results in a further degradation of the condition number by a factor . Received December 15, 1998 / Revised version received March 26, 1999 / Published online March 16, 2000