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Displaying 1321 –
1340 of
9187
We present an a posteriori error analysis of adaptive finite
element approximations of distributed control problems for second
order elliptic boundary value problems under bound constraints on
the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element
residuals. Since we do not assume any regularity of the data of
the problem, the error analysis further invokes data oscillations.
We prove reliability and efficiency of the error estimator...
We derive a residual based a posteriori error estimate for the Stokes-Brinkman problem on a two-dimensional polygonal domain. We use Taylor-Hood triangular elements. The link to the possible information on the regularity of the problem is discussed.
We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.
Zeta-generalized-Euler-constant functions,
and
defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and
(1) = ln
, are studied and estimated with high accuracy.
Lagrangian and augmented Lagrangian methods for nondifferentiable
optimization problems that arise from the total bounded variation formulation
of image restoration problems are analyzed. Conditional convergence of the
Uzawa algorithm and unconditional convergence of the first order augmented
Lagrangian schemes are discussed. A Newton type method based on an active
set strategy defined by means of the dual variables is developed and
analyzed. Numerical examples for blocky signals and images perturbed
by...
We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...
The minimization of nonconvex functionals naturally arises in
materials sciences where deformation gradients in certain alloys exhibit
microstructures. For example, minimizing sequences of the nonconvex
Ericksen-James energy can be associated with deformations in
martensitic materials that
are observed in experiments[2,3].
— From the numerical
point of view, classical conforming and nonconforming finite element
discretizations have been observed to give minimizers
with their quality being highly
dependent...
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments...
In this article we introduce an adaptive multi-level
method in space and time for convection diffusion problems. The scheme
is based on a multi-level spatial splitting and the use of different
time-steps. The temporal discretization relies on the characteristics method.
We derive an a posteriori error estimate and design a corresponding
adaptive algorithm.
The efficiency of the multi-level method is illustrated by numerical experiments,
in particular for a convection-dominated problem.
Currently displaying 1321 –
1340 of
9187