Thursday, November 16, 9:30 am in room MTH 3206, University of Maryland,
College Park
A general a posteriori error estimate for approximations to
Hamilton-Jacobi equations
Prof. Todd Peterson
Department of Mathematical Sciences
George Mason University
peterson@it.gmu.edu
We will present a general a posteriori error estimate for approximations to
Hamilton-Jacobi equations of the form $u_t + H(\nabla u) = f$. Solutions of
such equations may be nonsmooth, hence one considers weak solutions, and
these may not be unique. One possible selection criterion is the notion of
viscosity solution of Crandall and Lions, and our analysis is based on their
techniques. Our estimate applies to a large class of approximations -- it
is not specific to a particular approximation scheme. We will review some
basic properties of HJ equations, the notion of viscosity solution, draw
analogues with conservation laws, and indicate the proof of the a posteriori
estimate.
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