Simultaneous space-time finite element methods for parabolic optimal control problems

TL;DR

This paper develops and evaluates stabilized space-time finite element methods on unstructured meshes for solving parabolic optimal control problems with $L_2$ regularization, providing a flexible numerical approach.

Contribution

It introduces a novel stabilized space-time finite element framework for parabolic optimal control problems on unstructured meshes.

Findings

Methods are stable and accurate on complex meshes

Numerical experiments validate theoretical convergence rates

Applicable to a wide range of parabolic control problems

Abstract

This work presents, analyzes and tests stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking parabolic optimal control problems with the standard $L_2$-regularization.