Jean-Luc
Guermond and Bojan
Popov
Title: Approximating PDEs in L1
Abstract: In this talk we will consider L1-based minimization methods for three different
problems:
(1) Ill-posed transport equations;
(2) Stationary Hamilton-Jacobi equations;
(3) Digital elevation maps for natural and urban terrain.
We will describe each of the three problems. In the case of stationary
Hamilton-Jacobi equations a convergence theory will be presented. We construct
approximate solutions in all cases using a special type of L1-based
minimization. The main features of our methods are that they are of arbitrary
polynomial order and the numerical solutions are oscillation free even when the
underlying data/solution has singularities.