Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem
Numerical Analysis
2023-05-11 v1 Numerical Analysis
Abstract
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the -cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains. Numerical results are shown for both -cycle and -cycle algorithms.
Cite
@article{arxiv.2305.06317,
title = {Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem},
author = {Sijing Liu},
journal= {arXiv preprint arXiv:2305.06317},
year = {2023}
}