DE Seminar: Keegan Kirk
George Mason University
Location
Mathematics/Psychology : 401
Date & Time
April 21, 2025, 11:00 am – 12:00 pm
Description
Title: How to
insulate optimally
Speaker: Keegan Kirk
Abstract: Given a
fixed amount of insulating material, how should one coat a heat-conducting body
to optimize its insulating properties? A rigorous asymptotic analysis reveals
this problem can be cast as a convex variational problem with a non-smooth
boundary term. As this boundary term is difficult to treat numerically, we
consider an equivalent (Fenchel) dual variational formulation more amenable to
discretization. We propose a numerical scheme to solve this dual formulation on
the basis of a discrete duality theory inherited by the Raviart-Thomas and
Crouzeix-Raviart finite elements, and show that the solution of the original
primal problem can be reconstructed locally from the discrete dual solution. We
discuss the a posteriori and a priori error analysis of our scheme, derive a
posteriori estimators based on convex optimality conditions, and present
numerical examples to verify theory. As an application, we consider the design
of an optimally insulated home.
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