Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem

Sijing Liu

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arXiv · 2305.06317

Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem

Sijing Liu

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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 $W$-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 $W$ -cycle and $V$-cycle algorithms.

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BibTeX RIS

Sijing Liu. 2023-05-10. Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem. https://arxiv.org/abs/2305.06317

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