Alexei Lozinski

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In this paper we derive two a posteriori upper bounds for the heat equation. A continuous, piecewise linear finite element discretization in space and the Crank-Nicolson method for the time discretization are used. The error due to the space discretization is derived using anisotropic interpolation estimates and a post-processing procedure. The error due to(More)
We describe the clinical and pathologic observations of a 45-year-old woman with linear porokeratosis who developed squamous cell carcinoma in lesional sites. The squamous cell carcinoma metastasized to a regional lymph node. This is the second case of metastatic squamous cell carcinoma reported in porokeratosis and the first reported in the linear variety.
– We derive an analytical expression for the lower bound of the concurrence of mixed quantum states of composite 2×K systems. In contrast to other, implicitly defined entanglement measures, the numerical evaluation of our bound is straightforward. We explicitly evaluate its tightness for general mixed states of 2 × 3 systems, and identify a large class of(More)
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done(More)
We present a new method [7] for numerically solving elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. We use a relaxed iterative method which consists in calculating successive corrections to the solution in patches of finite elements. We analyse the spectral properties of the iteration operator [6]. We show how(More)