{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:44:04Z","timestamp":1787330644738,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>In this paper, we develop a multigrid preconditioner for the discrete system of linear equations that results from the mixed formulation of the linear plane elasticity problem using the Arnold-Winther elements. This, in turn, can be reduced to the problem of finding a multigrid preconditioner for the form $(\\cdot,\\cdot)+(\\vdiv\\cdot,\\vdiv\\cdot)$ in the symmetric matrix space resulting from Arnold-Winther elements. Since the form is not uniformly elliptic, a Helmholtz-type decomposition is essential. The Arnold-Winther finite element space gives rise to nonnested multilevel spaces adding difficulty to the analysis. We prove that for the variable V-cycle multigrid preconditioner, the condition number of the preconditioned system is independent of the number of levels. The results of numerical experiments are also presented.<\/jats:p>","DOI":"10.1137\/040617820","type":"journal-article","created":{"date-parts":[[2006,3,27]],"date-time":"2006-03-27T21:00:21Z","timestamp":1143493221000},"page":"478-493","source":"Crossref","is-referenced-by-count":5,"title":["A Multigrid Preconditioner for the Mixed Formulation of Linear Plane Elasticity"],"prefix":"10.1137","volume":"44","author":[{"given":"Joseph E.","family":"Pasciak","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanqiu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167064"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00826-0"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050002"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01395876"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01379659"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100348"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(90)90168-L"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/nla.373"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01405194"},{"key":"R10","first-page":"520","volume":"152","author":"Bramble J. 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