Galerkin methods

Wednesday, February 16, 2011 - 2:30pm - 3:30pm
Bernardo Cockburn (University of Minnesota, Twin Cities)
Friday, December 3, 2010 - 2:45pm - 3:30pm
Ricardo Nochetto (University of Maryland)
In contrast to most of the existing theory of adaptive
element methods (AFEM), we design an AFEM for -Δ u =
with right hand side f in H -1 instead of
L2. This
two important consequences. First we formulate our AFEM in
natural space for f, which is nonlocal. Second, we show
decay rates for the data estimator are dominated by those
for the
solution u in the energy norm. This allows us to conclude
Friday, December 3, 2010 - 9:45am - 10:30am
Andreas Frommer (Bergische Universität-Gesamthochschule Wuppertal (BUGH))
In lattice QCD, a standard discretization of the Dirac operator is given by the Wilson-Dirac operator, representing a nearest neighbor coupling on a 4d torus with 3x4 variables per grid point. The operator is non-symmetric but (usually) positive definite. Its small eigenmodes are non-smooth due to the stochastic nature of the coupling coefficients. Solving systems with the Wilson-Dirac operator on state-of-the-art lattices, typically in the range of 32-64 grid points in each of the four dimensions, is one of the prominent supercomputer applications today.
Thursday, July 28, 2011 - 2:50pm - 3:10pm
Brett Barwick (University of South Carolina)
Quillen-Suslin package
Friday, July 29, 2011 - 9:00am - 9:30am
Claudiu Raicu (University of California, Berkeley)
Friday, November 5, 2010 - 12:00pm - 12:45pm
Bernardo Cockburn (University of Minnesota, Twin Cities)

In this talk, we discuss a new class of discontinuous Galerkin methods called hybridizable. Their distinctive feature is that the only globally-coupled degrees of freedom are those of the numerical trace of the scalar variable. This renders them efficiently implementable. Moreover, they are more precise than all other discontinuous Galerkin methods as thet share with mixed methods their superconvergence properties in the scalar variable and their optimal order of convergence for the vector variable.

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