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Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
This article presents new immersed finite element (IFE) methods for solving
the popular second order elliptic interface problems on structured Cartesian
meshes even if the involved interfaces have nontrivial geometries. These IFE
methods contain extra stabilization terms introduced only at interface edges
for penalizing the discontinuity in IFE functions. With the enhanced stability
due to the added penalty, not only these IFE methods can be proven to have the
optimal convergence rate in the H1-norm provided that the exact solution has
sufficient regularity, but also numerical results indicate that their
convergence rates in both the H1-norm and the L2-norm do not deteriorate when
the mesh becomes finer which is a shortcoming of the classic IFE methods in
some situations. Trace inequalities are established for both linear and
bilinear IFE functions that are not only critical for the error analysis of
these new IFE methods, but also are of a great potential to be useful in error
analysis for other IFE methods
Asymptotic normality of extreme value estimators on
Consider i.i.d. random elements on . We show that, under an
appropriate strengthening of the domain of attraction condition, natural
estimators of the extreme-value index, which is now a continuous function, and
the normalizing functions have a Gaussian process as limiting distribution. A
key tool is the weak convergence of a weighted tail empirical process, which
makes it possible to obtain the results uniformly on . Detailed examples
are also presented.Comment: Published at http://dx.doi.org/10.1214/009053605000000831 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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