Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem
In this paper we investigate multigrid methods for a quad-curl problem on graded meshes. The approach is based on the Hodge decomposition. The solution for the quad-curl problem is approximated by solving standard second-order elliptic problems and optimal error estimates are obtained on graded meshes. We prove the uniform convergence of the multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical results.
Publication Source (Journal or Book title)
Computational Methods in Applied Mathematics
Brenner, S., Cui, J., & Sung, L. (2019). Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem. Computational Methods in Applied Mathematics, 19 (2), 215-232. https://doi.org/10.1515/cmam-2019-0011