Numerical Methods for the Optimal Control of Scalar Conservation Laws

TL;DR

This paper develops and analyzes numerical schemes for optimizing scalar conservation laws, focusing on relaxation methods and convergence for higher-order discretizations in control problems.

Contribution

It introduces continuous and discretized relaxation schemes specifically designed for scalar conservation laws, with new convergence results for advanced discretization methods.

Findings

Numerical results demonstrate effectiveness in tracking problems with nonsmooth states.

Higher-order schemes show improved convergence properties.

Relaxation schemes facilitate optimization of nonlinear hyperbolic PDEs.

Abstract

We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present numerical results on tracking type problems with nonsmooth desired states and convergence results for higher--order spatial and temporal discretization schemes.