Graduate Student Seminar - Chris Finlay
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Speaker: Chris Finlay
Title: Numerical Schemes for PDEs
Abstract:
How are PDEs actually solved in the wild? In this Pizza Seminar, I will talk about how to coax a computer into giving you a fairly accurate representation of the true solution to a degenerate elliptic PDE, by building a numerical scheme to solve the PDE. We'll cover existence and uniqueness of solutions to the numerical scheme. Solutions of the numerical scheme will be "pretty good", in that they won't be too far from the true solution of the PDE. In addition, I'll discuss why it is important for numerical schemes to respect underlying properties of the PDE we're trying to solve. For example, I'll show that if the PDE has a comparison principle, the numerical scheme should also have a comparison principle.
The aim of this talk is to give a flavour of numerical analysis, that dirty subject in the twilight zone between engineering and analysis.