We develop multigrid methods for an elliptic distributed optimal control problem on convex domains that are robust with respect to a regularization parameter. We prove the uniform convergence of the W-cycle algorithm and demonstrate the performance of V-cycle and W-cycle algorithms through numerical experiments.
Publication Source (Journal or Book title)
Journal of Computational and Applied Mathematics
Brenner, S., Liu, S., & Sung, L. (2020). Multigrid methods for saddle point problems: Optimality systems. Journal of Computational and Applied Mathematics, 372 https://doi.org/10.1016/j.cam.2020.112733