The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method

Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322     

Analysis of numerical integration in p-version finite element eigenvalue approximation

We study the effect of numerical integration when the p-version of the finite element method is used to approximate the eigenpairs of elliptic partial differential operators. We obtain optimal orders of convergence for approximate eigenvalues and eigenvectors under a certain set of requirements on the quadrature rules employed. This is the same set of conditions that has been shown (in an earlier work) to be sufficient for the optimal approximation of the solutions of the corresponding source problems.     

Measurement of the Strong Interaction Shift and Width of the Ground State of Pionic Hydrogen

Hyperfine Interactions - An experiment to measure the strong interaction width (Γ1s ) and shift (ε1s ) of the ground state of pionic hydrogen (π?p), in order to determine the...     

Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Mild Solutions for the Stochastic Generalized Burgers–Huxley Equation

Journal of Theoretical Probability - In this work, we consider the stochastic generalized Burgers–Huxley equation perturbed by space–time white noise and discuss the global solvability...     

Locking effects in the finite element approximation of elasticity problems

Summary We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252     

The pionic hydrogen experiment at PSI

A new high-precision determination of the strong-interaction shift (∈_1s) and broadening (Γ_1s) of the ground state in pionic hydrogen (πH) has been started at PSI. This constitutes a direct measurement of the πN scattering lengths and is an important test of the methods of chiral perturbation theory.The experiment will be conducted in two steps. In the first step we aim for a precision of 0.2% for ∈_1s and 3% for Γ_1s. A new method of energy calibration is used: by measuring πH simultaneously with pionic oxygen (πO), systematic errors are suppressed. The goal for the second step is an accuracy of 1% for Γ_1s.     

Infrared study of the bacterial autoinducer N-hexanoyl-homoserine lactone (C6-HSL) in the gas-phase, water, and octanol solutions

The N-hexanoyl-homoserine lactone (C6-HSL) molecule has been investigated by means of infrared multiphoton dissociation (IRMPD) and Fourier-transform infrared spectroscopy (FT-IR) under different conditions in an attempt to mimic biological situations encountered in communication between bacteria for quorum sensing. The protonated molecular ion was studied in the gas-phase that corresponds to a solvent-free situation somewhat analogous to that encountered in the receptor. The simulation of the IRMPD spectrum of the isolated ion was then conducted by means of quantum chemistry calculations in vacuum. In the case of the neutral species, the FT-IR spectra were recorded in D(2)O, mimicking the cytosolic and extracellular media as well as in 1-octanol that is often used for simulation of cell membranes. The interpretation was conducted by considering a C6-HSL molecule in its endo or exo conformation hydrogen-bonded to, respectively, six D(2)O and four 1-octanol molecules. A satisfying agreement with the experimental FT-IR studies conducted in solution at room temperature was obtained as long as a continuum IEFPCM model was added to the explicit solvent environment.     

Design principles and error analysis for reduced-shear plate-bending finite elements

Summary. In this paper, we consider the problem of designing plate-bending elements which are free of shear locking. This phenomenon is known to afflict several elements for the Reissner-Mindlin plate model when the thickness of the plate is small, due to the inability of the approximating subspaces to satisfy the Kirchhoff constraint. To avoid locking, a “reduction operator” is often applied to the stress, to modify the variational formulation and reduce the effect of this constraint. We investigate the conditions required on such reduction operators to ensure that the approximability and consistency errors are of the right order. A set of sufficient conditions is presented, under which optimal errors can be obtained – these are derived directly, without transforming the problem via a Hemholtz decomposition, or considering it as a mixed method. Our analysis explicitly takes into account boundary layers and their resolution, and we prove, via an asymptotic analysis, that convergence of the finite element approximations will occur uniformly as , even on quasiuniform meshes. The analysis is carried out in the case of a free boundary, where the boundary layer is known to be strong. We also propose and analyze a simple post-processing scheme for the shear stress. Our general theory is used to analyze the well-known MITC elements for the Reissner-Mindlin plate. As we show, the theory makes it possible to analyze both straight and curved elements. We also analyze some other elements. Received June 19, 1995