Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds

Beyond Automynorcagrams

While doing research for an unrelated article, I stumbled upon Howard W. Bergerson\u27s 1975 article in Word Ways, Automynorcagrams . This is a logological form in which the nth word of the text must begin with the nth character in the text. According to Bergerson, the idea behind the automynorcagram is to create a self-propelling and partially self-replicating logological entity

Finding Fixed Point Combinators using Prolog

A Powerful New Strategy, Called the Kernel Method, Has Been Developed by Larry Wos and William McCune at Argonne National Laboratories, to Study Various Fixed-Point Properties within Certain Classes of Applicative Systems. We Present a Very Simple Prolog Reasoning System, Named JIST, Which Incorporates Both Stages of the Kernel Method into a Single Unified Program. Furthermore, the Prolog Tool Has Been Extended to Run within a Distributed Environment using the Linda Protocol

A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations

We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples