{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:38:00Z","timestamp":1762349880266,"version":"build-2065373602"},"reference-count":16,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>For a dual-dual formulation of a frictional contact problem in linear elasticity we present a mixed finite element method based on PEERS elements and we analyze the performance of a nested Uzawa algorithm.<\/jats:p>","DOI":"10.1515\/cmam-2024-0131","type":"journal-article","created":{"date-parts":[[2025,5,4]],"date-time":"2025-05-04T06:00:21Z","timestamp":1746338421000},"page":"759-775","source":"Crossref","is-referenced-by-count":0,"title":["A Nested Uzawa Solver for a Dual-Dual Mixed Finite Element Method for Frictional Contact Problems in Linear Elasticity"],"prefix":"10.1515","volume":"25","author":[{"given":"Michael","family":"Andres","sequence":"first","affiliation":[{"name":"Volkswagen AG , Group Innovation, P.\u2009O. Box 17773, 38436 Wolfsburg , Germany"}]},{"given":"Matthias","family":"Maischak","sequence":"additional","affiliation":[{"name":"Department of Mathematics , College of Engineering, Design and Physical Sciences (CEDPS) , Brunel University of London , UB8 3PH , Uxbridge , United Kingdom"}]},{"given":"Ernst P.","family":"Stephan","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics , Leibniz University Hannover , 30167 Hannover , Germany"}]}],"member":"374","published-online":{"date-parts":[[2025,4,30]]},"reference":[{"key":"2025110513331354963_j_cmam-2024-0131_ref_001","unstructured":"M.  Andres,\nDual-dual formulations for frictional contact problems in mechanics,\nPhD thesis, Institute of Applied Mathematics, Leibniz Universit\u00e4t Hannover, Hannover, 2011."},{"key":"2025110513331354963_j_cmam-2024-0131_ref_002","doi-asserted-by":"crossref","unstructured":"M.  Andres, M.  Maischak and E. P.  Stephan,\nDual-dual formulation for a contact problem with friction,\nComput. Methods Appl. Math. 16 (2016), no. 1, 1\u201316.","DOI":"10.1515\/cmam-2015-0021"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_003","unstructured":"M.  Andres, M.  Maischak and E. P.  Stephan,\nA priori error analysis of a dual-dual formulation for frictional contact problems,\n(2025), submitted."},{"key":"2025110513331354963_j_cmam-2024-0131_ref_004","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold, F.  Brezzi and J.  Douglas, Jr.,\nPEERS: A new mixed finite element for plane elasticity,\nJapan J. Appl. Math. 1 (1984), no. 2, 347\u2013367.","DOI":"10.1007\/BF03167064"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_005","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and G.  Dolzmann,\nA posteriori error estimates for mixed FEM in elasticity,\nNumer. Math. 81 (1998), no. 2, 187\u2013209.","DOI":"10.1007\/s002110050389"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_006","doi-asserted-by":"crossref","unstructured":"G. N.  Gatica and M.  Maischak,\nA posteriori error estimates for the mixed finite element method with Lagrange multipliers,\nNumer. Methods Partial Differential Equations 21 (2005), no. 3, 421\u2013450.","DOI":"10.1002\/num.20050"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_007","doi-asserted-by":"crossref","unstructured":"G. N.  Gatica, M.  Maischak and E. P.  Stephan,\nNumerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM,\nESAIM Math. Model. Numer. Anal. 45 (2011), no. 4, 779\u2013802.","DOI":"10.1051\/m2an\/2010102"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_008","unstructured":"R.  Glowinski, J.-L.  Lions and R.  Tr\u00e9moli\u00e8res,\nNumerical Analysis of Variational Inequalities,\nStud. Math. Appl. 8,\nNorth-Holland, Amsterdam, 1981."},{"key":"2025110513331354963_j_cmam-2024-0131_ref_009","doi-asserted-by":"crossref","unstructured":"J.  Gwinner and E. P.  Stephan,\nA boundary element procedure for contact problems in plane linear elastostatics,\nRAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 27 (1993), no. 4, 457\u2013480.","DOI":"10.1051\/m2an\/1993270404571"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_010","doi-asserted-by":"crossref","unstructured":"M.  Lonsing and R.  Verf\u00fcrth,\nOn the stability of BDMS and PEERS elements,\nNumer. Math. 99 (2004), no. 1, 131\u2013140.","DOI":"10.1007\/s00211-004-0547-4"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_011","unstructured":"M.  Maischak,\nFEM\/BEM methods for Signorini-type problems: Error analysis, adaptivity, preconditioners,\nHabilitation, Institute of Applied Mathematics, Leibniz University Hanover, Hannover, 2004."},{"key":"2025110513331354963_j_cmam-2024-0131_ref_012","doi-asserted-by":"crossref","unstructured":"J.-C.  N\u00e9d\u00e9lec,\nIntegral equations with nonintegrable kernels,\nIntegral Equations Operator Theory 5 (1982), no. 4, 562\u2013572.","DOI":"10.1007\/BF01694054"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_013","unstructured":"J.  Nocedal and S. J.  Wright,\nNumerical Optimization, 2nd ed.,\nSpringer Ser. Oper. Res. Financ. Eng.,\nSpringer, New York, 2006."},{"key":"2025110513331354963_j_cmam-2024-0131_ref_014","doi-asserted-by":"crossref","unstructured":"J. E.  Roberts and J.-M.  Thomas,\nMixed and hybrid methods,\nHandbook of Numerical Analysis, Vol. II,\nNorth-Holland, Amsterdam (1991), 523\u2013639.","DOI":"10.1016\/S1570-8659(05)80041-9"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_015","doi-asserted-by":"crossref","unstructured":"O.  Steinbach,\nNumerische N\u00e4herungsverfahren f\u00fcr elliptische Randwertprobleme, Finite Elemente und Randelemente,\nB. G. Teubner, Stuttgart, 2003.","DOI":"10.1007\/978-3-322-80054-1"},{"key":"2025110513331354963_j_cmam-2024-0131_ref_016","doi-asserted-by":"crossref","unstructured":"G. H.  Wang and L. H.  Wang,\nUzawa type algorithm based on dual mixed variational formulation,\nAppl. Math. Mech. 23 (2002), no. 7, 682\u2013688.","DOI":"10.1007\/BF02456972"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2024-0131\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2024-0131\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:34:56Z","timestamp":1762349696000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2024-0131\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,30]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,6,25]]},"published-print":{"date-parts":[[2025,10,1]]}},"alternative-id":["10.1515\/cmam-2024-0131"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2024-0131","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2025,4,30]]}}}