740 research outputs found
The necklace view of the self
In this paper, I provide a framework for accounting for the self, based on
a reconstruction of Galen Strawson’s “theory of SESMETs,” or the Pearl
view, with Barry Dainton’s continuous consciousness thesis. I argue that the
framework I provide adequately accounts for the self and is preferable to solely
adopting either Strawson’s or Dainton’s theory. I call my reconstruction the
“Necklace” view of the self
Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity
In this work we propose and analyze a numerical method for electrical
impedance tomography of recovering a piecewise constant conductivity from
boundary voltage measurements. It is based on standard Tikhonov regularization
with a Modica-Mortola penalty functional and adaptive mesh refinement using
suitable a posteriori error estimators of residual type that involve the state,
adjoint and variational inequality in the necessary optimality condition and a
separate marking strategy. We prove the convergence of the adaptive algorithm
in the following sense: the sequence of discrete solutions contains a
subsequence convergent to a solution of the continuous necessary optimality
system. Several numerical examples are presented to illustrate the convergence
behavior of the algorithm.Comment: 26 pages, 12 figure
Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection
In this work, we derive a reliable and efficient residual-typed error
estimator for the finite element approximation of a 2d cathodic protection
problem governed by a steady-state diffusion equation with a nonlinear boundary
condition. We propose a standard adaptive finite element method involving the
D\"{o}rfler marking and a minimal refinement without the interior node
property. Furthermore, we establish the contraction property of this adaptive
algorithm in terms of the sum of the energy error and the scaled estimator.
This essentially allows for a quasi-optimal convergence rate in terms of the
number of elements over the underlying triangulation. Numerical experiments are
provided to confirm this quasi-optimality
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