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The approach is based on the Hodge decomposition. The solution\nfor the quad-curl problem is approximated by solving standard second-order elliptic\nproblems and optimal error estimates are obtained on graded meshes. We prove the\nuniform convergence of the multigrid algorithm for the resulting discrete problem. The\nperformance of these methods is illustrated by numerical results.<\/jats:p>","DOI":"10.1515\/cmam-2019-0011","type":"journal-article","created":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T09:01:03Z","timestamp":1552381263000},"page":"215-232","source":"Crossref","is-referenced-by-count":14,"title":["Multigrid Methods Based on Hodge Decomposition for a Quad-Curl Problem"],"prefix":"10.1515","volume":"19","author":[{"given":"Susanne C.","family":"Brenner","sequence":"first","affiliation":[{"name":"Department of Mathematics and Center for Computation and Technology , Louisiana State University , Baton Rouge , LA 70803 , USA"}]},{"given":"Jintao","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Hong Kong"}]},{"given":"Li-yeng","family":"Sung","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Center for Computation and Technology , Louisiana State University , Baton Rouge , LA 70803 , USA"}]}],"member":"374","published-online":{"date-parts":[[2019,3,12]]},"reference":[{"key":"2023033110021974848_j_cmam-2019-0011_ref_001_w2aab3b7e3042b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"C.  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