Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem-Reference-Cited by-同舟云学术

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

Published:2019-03-12 Issue:2 Volume:19 Page:215-232
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Brenner Susanne C.¹,Cui Jintao²,Sung Li-yeng¹

Affiliation:

1. Department of Mathematics and Center for Computation and Technology , Louisiana State University , Baton Rouge , LA 70803 , USA

2. Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Hong Kong

Abstract

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.

Funder

National Natural Science Foundation of China

Division of Mathematical Sciences

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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