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Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem

  • Susanne C. Brenner EMAIL logo , Jintao Cui und Li-yeng Sung
Veröffentlicht/Copyright: 12. März 2019

Abstract

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.

MSC 2010: 65N30; 65N15; 35Q60

Award Identifier / Grant number: 11771367

Award Identifier / Grant number: DMS-16-20273

Funding statement: The work of the first and third authors was supported in part by the National Science Foundation under Grant No. DMS-16-20273. The second author’s work is supported in part by the National Natural Science Foundation of China (NSFC) Grant no. 11771367 and Hong Kong PolyU General Research Grant G-YBM.

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Received: 2019-01-22
Accepted: 2019-01-22
Published Online: 2019-03-12
Published in Print: 2019-04-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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