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.