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TZID:America/Chicago
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DTSTART:20231105T020000
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DTSTART:20240310T020000
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UID:calendar.25907.field_event_date_2.0@math.wustl.edu
CREATED:20231117T154235Z
DESCRIPTION:Abstract: We consider various finite element methods for numeri
cally solving PDE's, using several formulations of the Poisson problem as
examples. All fall under the framework of Galerkin methods, which provid
e approximate solutions by solving discrete versions of the problem. Confo
rming methods may have limitations on account of the continuity requiremen
ts of the spaces involved. Discontinuous Galerkin (DG) methods yield addit
ional flexibility but result in greater computational complexity. Hybridiz
able discontinuous Galerkin (HDG) methods address this issue using additio
nal unknowns, which create a nicer structure for the discrete problems,
allowing for an increase in efficiency via static condensation. For HDG me
thods for the Poisson problem, it has been shown that a property of the d
iscrete spaces called an 'M-decomposition' results in desirable properties
for the methods, including 'superconvergence'-the ability to define a ne
w approximation for one of the unknowns which converges as fast as the dif
ference between two approximations in the discrete space. Current research
focuses on whether these results apply in the setting of finite element e
xterior calculus (FEEC), a framework which encompasses many known methods
for certain problems as well as methods which have yet to be studied in d
etail.
DTSTART;TZID=America/Chicago:20231120T140000
DTEND;TZID=America/Chicago:20231120T150000
LAST-MODIFIED:20231117T154235Z
SUMMARY:Analysis Seminar: Finite element methods and superconvergence
URL;TYPE=URI:https://math.wustl.edu/events/analysis-seminar-finite-element-
methods-and-superconvergence
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