Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow

We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite general and shows promise for application to stabilized nonlinear problems, such as Burger's equation and the incompressible Navier-Stokes equations, as well as potential for compressible flow problems.Singapore-MIT Alliance (SMA

Aerodynamic fuze characteristics for trajectory control

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.Includes bibliographical references (p. 131-135).by Alexander Michael Budge.M.S

Computing upper and lower bounds on linear functional outputs from linear coercive partial differential equations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2003.Includes bibliographical references (p. 115-123).Uncertainty about the reliability of numerical approximations frequently undermines the utility of field simulations in the engineering design process: simulations are often not trusted because they lack reliable feedback on accuracy, or are more costly than needed because they are performed with greater fidelity than necessary in an attempt to bolster trust. In addition to devitalized confidence, numerical uncertainty often causes ambiguity about the source of any discrepancies when using simulation results in concert with experimental measurements. Can the discretization error account for the discrepancies, or is the underlying continuum model inadequate? This thesis presents a cost effective method for computing guaranteed upper and lower bounds on the values of linear functional outputs of the exact weak solutions to linear coercive partial differential equations with piecewise polynomial forcing posed on polygonal domains. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element discretizations to calculate a primal and an adjoint solution along with well known hybridization techniques to calculate interelement continuity multipliers. At the heart of the method lies a local dual problem by which we transform an infinite-dimensional minimization problem into a finite-dimensional feasibility problem.(cont.) The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the H¹-norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The complete procedure computes approximate outputs to a given precision in polynomial time. Local information generated by the procedure can be used as an adaptive meshing indicator. We apply the method to Poisson's equation and the steady-state advection-diffusion-reaction equation.by Alexander M. Sauer-Budge.Ph.D

Entrances and exits: changing perceptions of primary teaching as a career for men

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713640830~db=all Copyright Informa / Taylor and Francis. DOI: 10.1080/03004430802352087The number of men in teaching has always been small, particularly in early childhood, but those that do come into teaching usually do so for the same reasons as women, namely enjoyment of working with children, of wanting to teach and wanting to make a difference to children's lives. However, in two separate studies, the authors have shown that on beginning teacher training in 1998, and at the point of leaving the profession in 2005, men and women tend to emphasise different concerns. This article will explore those differences and seek possible explanations for how men's views of teaching might be changing over time.Peer reviewe

Democratic cultural policy : democratic forms and policy consequences

The forms that are adopted to give practical meaning to democracy are assessed to identify what their implications are for the production of public policies in general and cultural policies in particular. A comparison of direct, representative, democratic elitist and deliberative versions of democracy identifies clear differences between them in terms of policy form and democratic practice. Further elaboration of these differences and their consequences are identified as areas for further research