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TITLE

A numerical analyst's journey through spacetime.

ABSTRACT

Physical laws are elegantly described through partial differential equations (PDE). A core concern in numerical analysis is how to achieve high-order approximations of solutions to these PDE. We need to ensure our approximation strategy leads to a consistent, stable and convergent method. One design principle is that of structure-preservation: our discrete problem should respect important underlying structures in the problem. These structures could be geometrical, algebraic, topological, and homological. In this talk I'll introduce the powerful finite element approach for PDE, and then motivate the need for the beautiful mathematical theory of the finite element exterior calculus. These powerful ideas allow us to describe polynomial differential forms - which themselves form finite-dimensional subcomplexes of the deRham complex. These are typically described on simplicial or tensorial domains. After some concrete examples in R^2 and R^3, I'll use these ideas to describe recent work on the design of high-order discretizations of PDEs in R^4 (space-time problems). I'll present families of conforming high-order finite elements on simplicial elements (these are well-known), and also on certain non-simplicial domains. The constructions - which are explicit - rely on techniques from the finite element exterior calculus. This is joint work with David Williams.

PLACE
Hybride - CRM, Salle / Room 6214, Pavillon Andr茅 Aisenstadt