{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T18:04:56Z","timestamp":1649181896178},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,6,21]],"date-time":"2015-06-21T00:00:00Z","timestamp":1434844800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2016,4]]},"DOI":"10.1007\/s00211-015-0736-3","type":"journal-article","created":{"date-parts":[[2015,6,20]],"date-time":"2015-06-20T02:25:35Z","timestamp":1434767135000},"page":"631-655","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The BEM with graded meshes for the electric field integral equation on polyhedral surfaces"],"prefix":"10.1007","volume":"132","author":[{"given":"A.","family":"Bespalov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Nicaise","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,6,21]]},"reference":[{"key":"736_CR1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1090\/S0025-5718-2010-02406-8","volume":"80","author":"G Acosta","year":"2011","unstructured":"Acosta, G., Apel, T., Dur\u00e1n, R.G., Lombardi, A.L.: Error estimates for Raviart\u2013Thomas interpolation of any order on anisotropic tetrahedra. Math. Comput. 80, 141\u2013163 (2011)","journal-title":"Math. Comput."},{"key":"736_CR2","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1137\/S0036142997330809","volume":"36","author":"M Ainsworth","year":"1999","unstructured":"Ainsworth, M., McLean, W., Tran, T.: The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. SIAM J. Numer. Anal. 36, 1901\u20131932 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"736_CR3","unstructured":"Apel, T.: Anisotropic Finite Elements: Local Estimates and Applications. Advances in Numerical Mathematics, Teubner (1999)"},{"key":"736_CR4","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.apnum.2010.03.012","volume":"60","author":"A Bespalov","year":"2010","unstructured":"Bespalov, A., Heuer, N.: The $$hp$$ h p -BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis. Appl. Numer. Math. 60, 705\u2013718 (2010)","journal-title":"Appl. Numer. Math."},{"key":"736_CR5","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1093\/imanum\/drn072","volume":"30","author":"A Bespalov","year":"2010","unstructured":"Bespalov, A., Heuer, N.: Natural $$p$$ p -BEM for the electric field integral equation on screens. IMA J. Numer. Anal. 30, 595\u2013628 (2010)","journal-title":"IMA J. Numer. Anal."},{"key":"736_CR6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1051\/m2an\/2010039","volume":"45","author":"A Bespalov","year":"2011","unstructured":"Bespalov, A., Heuer, N.: A new $${\\mathbf{H}}({\\rm div})$$ H ( div ) -conforming $$p$$ p -interpolation operator in two dimensions. ESAIM. Math. Model. Numer. Anal. 45, 255\u2013275 (2011)","journal-title":"ESAIM. Math. Model. Numer. Anal."},{"key":"736_CR7","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1002\/num.20688","volume":"28","author":"A Bespalov","year":"2012","unstructured":"Bespalov, A., Heuer, N.: Natural $$hp$$ h p -BEM for the electric field integral equation with singular solutions. Numer. Methods Partial Differ. Equ. 28, 1466\u20131480 (2012)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"736_CR8","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1137\/090766620","volume":"48","author":"A Bespalov","year":"2010","unstructured":"Bespalov, A., Heuer, N., Hiptmair, R.: Convergence of the natural $$hp$$ h p -BEM for the electric field integral equation on polyhedral surfaces. SIAM J. Numer. Anal. 48, 1518\u20131529 (2010)","journal-title":"SIAM J. Numer. Anal."},{"key":"736_CR9","doi-asserted-by":"crossref","unstructured":"Bespalov, A., Nicaise, S.: The BEM with graded meshes for the electric field integral equation on polyhedral surfaces (2015, preprint). arXiv:1504.02647v1 [math.NA]","DOI":"10.1007\/s00211-015-0736-3"},{"key":"736_CR10","unstructured":"Bespalov, A., Nicaise, S.: A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedra (in preparation)"},{"key":"736_CR11","doi-asserted-by":"crossref","unstructured":"Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol. 15. Springer, New York (1991)","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"736_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S003614290342385X","volume":"43","author":"A Buffa","year":"2005","unstructured":"Buffa, A.: Remarks on the discretization of some noncoercive operator with applications to heterogeneous Maxwell equations. SIAM J. Numer. Anal. 43, 1\u201318 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"736_CR13","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s00211-002-0422-0","volume":"94","author":"A Buffa","year":"2003","unstructured":"Buffa, A., Christiansen, S.H.: The electric field integral equation on Lipschitz screens: definitions and numerical approximation. Numer. Math. 94, 229\u2013267 (2003)","journal-title":"Numer. Math."},{"key":"736_CR14","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1002\/1099-1476(20010110)24:1<9::AID-MMA191>3.0.CO;2-2","volume":"24","author":"A Buffa","year":"2001","unstructured":"Buffa, A., Ciarlet Jr, P.: On traces for functional spaces related to Maxwell\u2019s equations, part I: an integration by parts formula in Lipschitz polyhedra. Math. Methods Appl. Sci. 24, 9\u201330 (2001)","journal-title":"Math. Methods Appl. Sci."},{"key":"736_CR15","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/1099-1476(20010110)24:1<31::AID-MMA193>3.0.CO;2-X","volume":"24","author":"A Buffa","year":"2001","unstructured":"Buffa, A., Ciarlet Jr, P.: On traces for functional spaces related to Maxwell\u2019s equations, part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications. Math. Methods Appl. Sci. 24, 31\u201348 (2001)","journal-title":"Math. Methods Appl. Sci."},{"key":"736_CR16","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s002110100372","volume":"92","author":"A Buffa","year":"2002","unstructured":"Buffa, A., Costabel, M., Schwab, C.: Boundary element methods for Maxwell\u2019s equations on non-smooth domains. Numer. Math. 92, 679\u2013710 (2002)","journal-title":"Numer. Math."},{"key":"736_CR17","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/S0022-247X(02)00455-9","volume":"276","author":"A Buffa","year":"2002","unstructured":"Buffa, A., Costabel, M., Sheen, D.: On traces for H(curl, $$\\Omega $$ \u03a9 ) in Lipschitz domains. J. Math. Anal. Appl. 276, 845\u2013867 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"736_CR18","doi-asserted-by":"crossref","unstructured":"Buffa, A., Hiptmair, R.: Galerkin boundary element methods for electromagnetic scattering. In: Topics in Computational Wave Propagation, Lect. Notes Comput. Sci. Eng., vol. 31, pp. 83\u2013124. Springer, Berlin (2003)","DOI":"10.1007\/978-3-642-55483-4_3"},{"key":"736_CR19","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s00211-002-0407-z","volume":"95","author":"A Buffa","year":"2003","unstructured":"Buffa, A., Hiptmair, R., von Petersdorff, T., Schwab, C.: Boundary element methods for Maxwell transmission problems in Lipschitz domains. Numer. Math. 95, 459\u2013485 (2003)","journal-title":"Numer. Math."},{"key":"736_CR20","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s002050050197","volume":"151","author":"M Costabel","year":"2000","unstructured":"Costabel, M., Dauge, M.: Singularities of electromagnetic fields in polyhedral domains. Arch. Rational Mech. Anal. 151, 221\u2013276 (2000)","journal-title":"Arch. Rational Mech. Anal."},{"key":"736_CR21","volume-title":"Elliptic Problems in Nonsmooth Domains","author":"P Grisvard","year":"1985","unstructured":"Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Pitman Publishing Inc., Boston (1985)"},{"key":"736_CR22","unstructured":"Grisvard, P.: Singularities in Boundary Value Problems, Research Notes in Applied Mathematics, vol. 22. Masson, Paris (1992)"},{"key":"736_CR23","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1137\/S0036142901397757","volume":"41","author":"R Hiptmair","year":"2003","unstructured":"Hiptmair, R.: Coupling of finite elements and boundary elements in electromagnetic scattering. SIAM J. Numer. Anal. 41, 919\u2013944 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"736_CR24","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1137\/S0036142901387580","volume":"40","author":"R Hiptmair","year":"2002","unstructured":"Hiptmair, R., Schwab, C.: Natural boundary element methods for the electric field integral equation on polyhedra. SIAM J. Numer. Anal. 40, 66\u201386 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"736_CR25","volume-title":"Non-Homogeneous Boundary Value Problems and Applications I","author":"JL Lions","year":"1972","unstructured":"Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications I. Springer, New York (1972)"},{"key":"736_CR26","volume-title":"Strongly Elliptic Systems and Boundary Integral Equations","author":"W McLean","year":"2000","unstructured":"McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)"},{"key":"736_CR27","unstructured":"von Petersdorff, T.: Randwertprobleme der Elastizit\u00e4tstheorie f\u00fcr Polyeder\u2014Singularit\u00e4ten und Approximation mit Randelementmethoden, PhD thesis. Technische Hochschule Darmstadt (1989)"},{"key":"736_CR28","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/mma.1670120306","volume":"12","author":"T Petersdorff von","year":"1990","unstructured":"von Petersdorff, T., Stephan, E.P.: Regularity of mixed boundary value problems in $$\\mathbb{R}^3$$ R 3 and boundary element methods on graded meshes. Math. Methods Appl. Sci. 12, 229\u2013249 (1990)","journal-title":"Math. Methods Appl. Sci."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0736-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-015-0736-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0736-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T12:05:41Z","timestamp":1566907541000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-015-0736-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,21]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["736"],"URL":"https:\/\/doi.org\/10.1007\/s00211-015-0736-3","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,21]]}}}