{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T04:24:33Z","timestamp":1680323073988},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T00:00:00Z","timestamp":1678320000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for interface problems in nonlinear elasticity.\nIt concerns \ud835\udc5d-Laplacian-type Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media.\nWe propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary\/domain variational inequality.<\/jats:p>","DOI":"10.1515\/cmam-2022-0120","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T12:51:28Z","timestamp":1678279888000},"page":"389-404","source":"Crossref","is-referenced-by-count":1,"title":["Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems"],"prefix":"10.1515","volume":"23","author":[{"given":"Heiko","family":"Gimperlein","sequence":"first","affiliation":[{"name":"Engineering Mathematics , University of Innsbruck , Technikerstra\u00dfe 13, 6020 Innsbruck , Austria"}]},{"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":[[2023,3,9]]},"reference":[{"key":"2023033113095773248_j_cmam-2022-0120_ref_001","doi-asserted-by":"crossref","unstructured":"S. N. Antontsev, J. I. D\u00edaz and S. Shmarev,\nEnergy Methods for Free Boundary Problems. Applications to Nonlinear PDEs and Fluid Mechanics,\nProgr. Nonlinear Differential Equations Appl. 48,\nBirkh\u00e4user, Boston, 2002.","DOI":"10.1115\/1.1483358"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_002","unstructured":"G. Astarita and G. Marrucci,\nPrinciples of Non-Newtonian fluid Mechanics,\nMcGraw-Hill, New York, 1974."},{"key":"2023033113095773248_j_cmam-2022-0120_ref_003","unstructured":"C. Atkinson and C. R. Champion,\nSome boundary-value problems for the equation \n                  \n                     \n                        \n                           \n                              \u2207\n                              \u22c5\n                              \n                                 (\n                                 \n                                    \n                                       \n                                          |\n                                          \n                                             \u2207\n                                             \u03c6\n                                          \n                                          |\n                                       \n                                       N\n                                    \n                                    \u2062\n                                    \n                                       \u2207\n                                       \u03c6\n                                    \n                                 \n                                 )\n                              \n                           \n                           =\n                           0\n                        \n                     \n                     \n                     \\nabla\\cdot(\\lvert\\nabla\\varphi\\rvert^{N}\\nabla\\varphi)=0\n                  \n               ,\nQuart. J. Mech. Appl. Math. 37 (1984), no. 3, 401\u2013419."},{"key":"2023033113095773248_j_cmam-2022-0120_ref_004","doi-asserted-by":"crossref","unstructured":"C. Atkinson and W. Jones,\nSimilarity solutions in some non-linear diffusion problems and in boundary layer flow of a pseudo plastic fluid,\nQuart J. Mech. Appl. Math. 27 (1974), 193\u2013211.","DOI":"10.1093\/qjmam\/27.2.193"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_005","doi-asserted-by":"crossref","unstructured":"L. Banz, H. Gimperlein, A. Issaoui and E. P. Stephan,\nStabilized mixed \n                  \n                     \n                        \n                           h\n                           \u2062\n                           p\n                        \n                     \n                     \n                     hp\n                  \n               -BEM for frictional contact problems in linear elasticity,\nNumer. Math. 135 (2017), no. 1, 217\u2013263.","DOI":"10.1007\/s00211-016-0797-y"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_006","doi-asserted-by":"crossref","unstructured":"J. W. Barrett and W. B. Liu,\nFinite element error analysis of a quasi-Newtonian flow obeying the Carreau or power law,\nNumer. Math. 64 (1993), no. 4, 433\u2013453.","DOI":"10.1007\/BF01388698"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_007","doi-asserted-by":"crossref","unstructured":"S. C. Brenner and L. R. Scott,\nThe Mathematical Theory of Finite Element Methods,\nTexts Appl. Math. 15,\nSpringer, New York, 1994.","DOI":"10.1007\/978-1-4757-4338-8"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_008","doi-asserted-by":"crossref","unstructured":"C. Carstensen,\nA posteriori error estimate for the symmetric coupling of finite elements and boundary elements,\nComputing 57 (1996), no. 4, 301\u2013322.","DOI":"10.1007\/BF02252251"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_009","doi-asserted-by":"crossref","unstructured":"C. Carstensen, S. A. Funken and E. P. Stephan,\nOn the adaptive coupling of FEM and BEM in 2-d-elasticity,\nNumer. Math. 77 (1997), no. 2, 187\u2013221.","DOI":"10.1007\/s002110050283"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_010","doi-asserted-by":"crossref","unstructured":"M. Costabel,\nBoundary integral operators on Lipschitz domains: elementary results,\nSIAM J. Math. Anal. 19 (1988), no. 3, 613\u2013626.","DOI":"10.1137\/0519043"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_011","doi-asserted-by":"crossref","unstructured":"J. C. De Los Reyes and M. 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I,\nBirkh\u00e4user, Basel, 1983.","DOI":"10.1007\/978-3-0346-0416-1"},{"key":"2023033113095773248_j_cmam-2022-0120_ref_029","doi-asserted-by":"crossref","unstructured":"H. Triebel,\nTheory of Function Spaces. 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