On the use of elliptic regularity theory for the numerical solution of variational problems

TL;DR

This paper explores how elliptic regularity theory enhances the development of numerical methods for solving variational problems, including multiobjective control and contact mechanics boundary value problems.

Contribution

It demonstrates the importance of elliptic regularity theory in designing efficient numerical solutions for complex variational problems.

Findings

Elliptic regularity theory improves numerical method efficiency.

Application to multiobjective optimal control problems.

Application to elliptic variational inequalities in contact mechanics.

Abstract

In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control problems that can be formulated as jointly convex generalized Nash equilibrium problems and to nonsmooth boundary value problems that stem from contact mechanics leading to elliptic variational inequalities.