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lecture image Computational Mathematics Seminar Series
A discontinuous Galerkin finite element method for Hamilton–Jacobi–Bellman equations on piecewise curved domains, with applications to Monge–Ampère type equations
Ellya Kawecki, Oxford University
Postgraduate Student
Digital Media Center 1034
February 22, 2018 - 03:30 pm
Abstract:
We introduce a discontinuous Galerkin finite element method (DGFEM) for Hamilton–Jacobi–Bellman equations on piecewise curved domains, and prove that the method is consistent, stable, and produces optimal convergence rates. Upon utilising a long standing result due to N. Krylov, we may characterise the Monge–Ampère equation as a HJB equation; in two dimensions, this HJB equation can be characterised further as uniformly elliptic HJB equation, allowing for the application of the DGFEM.
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Speaker's Bio:
I am a current member of the Oxford University Partial Differential Equations (PDEs) Centre for Doctoral Training, specialising in the numerical analysis of PDEs. My research interests fall under the analysis of numerical methods for fully nonlinear elliptic equations, in particular, Hamilton-Jacobi-Bellman and Monge-Ampère type equations. I am also interested in the analysis of numerical methods for linear elliptic equations in nondivergence form with Dirichlet and oblique boundary conditions.
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This lecture has refreshments @ 03:00 pm