A mollified Ensemble Kalman filter. (arXiv:1002.3091v1 [math.NA])

A mollified Ensemble Kalman filter. (arXiv:1002.3091v1 [math.NA]): "

It is well recognized that discontinuous analysis increments of sequential
data assimilation systems, such as ensemble Kalman filters, might lead to
spurious high frequency adjustment processes in the model dynamics. Various
methods have been devised to continuously spread out the analysis increments
over a fixed time interval centered about analysis time. Among these techniques
are nudging and incremental analysis updates (IAU). Here we propose another
alternative, which may be viewed as a hybrid of nudging and IAU and which
arises naturally from a recently proposed continuous formulation of the
ensemble Kalman analysis step. A new slow-fast extension of the popular
Lorenz-96 model is introduced to demonstrate the properties of the proposed
mollified ensemble Kalman filter.

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A geometric approach to error estimates for conservation laws posed on a spacetime. (arXiv:1002.3137v1 [math.AP])

A geometric approach to error estimates for conservation laws posed on a spacetime. (arXiv:1002.3137v1 [math.AP]): "

We consider a hyperbolic conservation law posed on an (N+1)-dimensional
spacetime, whose flux is a field of differential forms of degree N.
Generalizing the classical Kuznetsov's method, we derive an L1 error estimate
which applies to a large class of approximate solutions. In particular, we
apply our main theorem and deal with two entropy solutions associated with
distinct flux fields, as well as with an entropy solution and an approximate
solution. Our framework encompasses, for instance, equations posed on a
globally hyperbolic Lorentzian manifold.

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Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues. (arXiv:1002.2950v1 [math.AP])

Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues. (arXiv:1002.2950v1 [math.AP]): "

Kinetic relations are required in order to characterize nonclassical
undercompressive shock waves and formulate a well-posed initial value problem
for nonlinear hyperbolic systems of conservation laws. Such nonclassical waves
arise in weak solutions of a large variety of physical models: phase
transitions, thin liquid films, magnetohydrodynamics, Camassa-Holm model,
martensite-austenite materials, semi-conductors, combustion theory, etc. This
review presents the research done in the last fifteen years which led the
development of the theory of kinetic relations for undercompressive shocks and
has now covered many physical, mathematical, and numerical issues. The main
difficulty overcome here in our analysis of nonclassical entropy solutions
comes from their lack of monotonicity with respect to initial data.
Undercompressive shocks of hyperbolic conservation laws turn out to exhibit
features that are very similar to shocks of nonconservative hyperbolic systems,
who were investigated earlier by the author.

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