Adjoint methods for obstacle problems and weakly coupled systems of PDE

TL;DR

This paper applies the adjoint method to obstacle problems and weakly coupled PDE systems, providing new insights into convergence rates of approximation methods.

Contribution

It extends the adjoint method to obstacle problems and coupled systems, offering novel convergence results for approximation procedures.

Findings

Derived new convergence speed results for approximation methods.

Applied the adjoint method to obstacle and coupled PDE systems.

Enhanced understanding of solution behaviors in complex PDE systems.

Abstract

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton-Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of common approximation procedures are derived.