Eitan Tadmor
ENO reconstruction and ENO interpolation are stable.
Wed, 12/07/2011 - 15:01 — SomNambulAuthors: Eitan Tadmor, Ulrik S. Fjordholm, Siddhartha Mishra
Subjects: Numerical Analysis
AbstractWe prove stability estimates for the ENO reconstruction and ENO interpolation
procedures. In particular, we show that the jump of the reconstructed ENO
pointvalues at each cell interface has the same sign as the jump of the
underlying cell averages across that interface. We also prove that the jump of
the reconstructed values can be upper-bounded in terms of the jump of the
underlying cell averages. Similar sign properties hold for the ENO
interpolation procedure.Hierarchical solutions for linear equations: a constructive proof of the closed range theorem.
Tue, 03/09/2010 - 16:01 — SomNambulAuthors: Eitan Tadmor
Subjects: Analysis of PDEs
AbstractWe construct uniformly bounded solutions for the equations div U=f and curl
U= f in the critical cases f \in L^d_#(T^d,R) and f\in L^3_#(R^3,R^3). Bourgain
& Brezis, \cite{BB03,BB07}, have shown that there exists no \emph{linear}
construction for such solutions. Our constructions are special cases of a
general framework for solving linear equations of the form T U=f, where T is a
linear operator densely defined in Banach space B with a closed range in a
(proper subspace) of Lebesgue space L^p_#(\Omega), and with an injective dual
T^*.
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