14,025 research outputs found
A high accuracy Leray-deconvolution model of turbulence and its limiting behavior
In 1934 J. Leray proposed a regularization of the Navier-Stokes equations
whose limits were weak solutions of the NSE. Recently, a modification of the
Leray model, called the Leray-alpha model, has atracted study for turbulent
flow simulation. One common drawback of Leray type regularizations is their low
accuracy. Increasing the accuracy of a simulation based on a Leray
regularization requires cutting the averaging radius, i.e., remeshing and
resolving on finer meshes. This report analyzes a family of Leray type models
of arbitrarily high orders of accuracy for fixed averaging radius. We establish
the basic theory of the entire family including limiting behavior as the
averaging radius decreases to zero, (a simple extension of results known for
the Leray model). We also give a more technically interesting result on the
limit as the order of the models increases with fixed averaging radius. Because
of this property, increasing accuracy of the model is potentially cheaper than
decreasing the averaging radius (or meshwidth) and high order models are doubly
interesting
Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Over the past few decades, there has been substantial interest in evolution
equations that involving a fractional-order derivative of order
in time, due to their many successful applications in
engineering, physics, biology and finance. Thus, it is of paramount importance
to develop and to analyze efficient and accurate numerical methods for reliably
simulating such models, and the literature on the topic is vast and fast
growing. The present paper gives a concise overview on numerical schemes for
the subdiffusion model with nonsmooth problem data, which are important for the
numerical analysis of many problems arising in optimal control, inverse
problems and stochastic analysis. We focus on the following aspects of the
subdiffusion model: regularity theory, Galerkin finite element discretization
in space, time-stepping schemes (including convolution quadrature and L1 type
schemes), and space-time variational formulations, and compare the results with
that for standard parabolic problems. Further, these aspects are showcased with
illustrative numerical experiments and complemented with perspectives and
pointers to relevant literature.Comment: 24 pages, 3 figure
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
This report is a collection of comments on the Read Paper of Fearnhead and
Prangle (2011), to appear in the Journal of the Royal Statistical Society
Series B, along with a reply from the authors.Comment: 10 page
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