{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T12:54:29Z","timestamp":1762865669245},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2010,9]]},"DOI":"10.1007\/s10915-010-9366-1","type":"journal-article","created":{"date-parts":[[2010,4,23]],"date-time":"2010-04-23T18:17:54Z","timestamp":1272046674000},"page":"219-254","source":"Crossref","is-referenced-by-count":36,"title":["Optimal Penalty Parameters for Symmetric Discontinuous Galerkin Discretisations of\u00a0the\u00a0Time-Harmonic Maxwell Equations"],"prefix":"10.1007","volume":"44","author":[{"given":"D.","family":"S\u00e1rm\u00e1ny","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Izs\u00e1k","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. J. W.","family":"van\u00a0der Vegt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,4,24]]},"reference":[{"issue":"14","key":"9366_CR1","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1002\/nme.847","volume":"58","author":"M. Ainsworth","year":"2003","unstructured":"Ainsworth, M., Coyle, J.: Hierarchic finite element bases on unstructured tetrahedral meshes. Int. J. Numer. Methods Eng. 58(14), 2103\u20132130 (2003)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"9366_CR2","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D.N. Arnold","year":"2001","unstructured":"Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749\u20131779 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"9366_CR3","unstructured":"Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page (2001). http:\/\/www.mcs.anl.gov\/petsc"},{"key":"9366_CR4","unstructured":"Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S., Savini, M.: A high order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Proceedings of the 1997 2nd European Conference on Turbomachinery\u2014Fluid Dynamics and Thermodynamics (Antwerpen, Belgium), pp.\u00a099\u2013108 (1997)"},{"issue":"1","key":"9366_CR5","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/20.43860","volume":"24","author":"A. Bossavit","year":"1988","unstructured":"Bossavit, A.: A rationale for \u2018edge-elements\u2019 in 3-D fields computations. IEEE Trans. Magn. 24(1), 74\u201379 (1988)","journal-title":"IEEE Trans. Magn."},{"issue":"2","key":"9366_CR6","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/20.106414","volume":"26","author":"A. Bossavit","year":"1990","unstructured":"Bossavit, A.: Solving Maxwell equations in a closed cavity, and the question of \u2018spurious modes\u2019. IEEE Trans. Magn. 26(2), 702\u2013705 (1990)","journal-title":"IEEE Trans. Magn."},{"key":"9366_CR7","series-title":"Lect. Notes Comput. Sci. Eng.","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/978-3-642-56470-3_9","volume-title":"Scientific computing in electrical engineering","author":"A. Bossavit","year":"2001","unstructured":"Bossavit, A.: On the representation of differential forms by potentials in dimension 3. In: Scientific computing in electrical engineering, Warnem\u00fcnde, 2000. Lect. Notes Comput. Sci. Eng., vol.\u00a018, pp.\u00a097\u2013104. Springer, Berlin (2001)"},{"key":"9366_CR8","unstructured":"Brezzi, F., Manzini, G., Marini, D., Pietra, P., Russo, A.: Discontinuous finite elements for diffusion problems. In: Atti Convegno in onore di F. Brioschi, Milan, 1997, pp.\u00a0197\u2013217. Istitutto Lombardo, Accademia di Scienza e Lettere, Milan, Italy, 1999"},{"issue":"5","key":"9366_CR9","doi-asserted-by":"crossref","first-page":"2198","DOI":"10.1137\/050636887","volume":"44","author":"A. Buffa","year":"2006","unstructured":"Buffa, A., Perugia, I.: Discontinuous Galerkin approximation of the Maxwell eigenproblem. SIAM J. Numer. Anal. 44(5), 2198\u20132226 (2006)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9366_CR10","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.cam.2006.01.042","volume":"204","author":"A. Buffa","year":"2007","unstructured":"Buffa, A., Houston, P., Perugia, I.: Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. J.\u00a0Comput. Appl. Math. 204(2), 317\u2013333 (2007)","journal-title":"J.\u00a0Comput. Appl. Math."},{"issue":"1\u20133","key":"9366_CR11","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s10915-008-9238-0","volume":"40","author":"A. Buffa","year":"2009","unstructured":"Buffa, A., Perugia, I., Warburton, T.: The mortar-discontinuous Galerkin method for the 2D Maxwell eigenproblem. J.\u00a0Sci. Comput. 40(1\u20133), 86\u2013114 (2009). Available at http:\/\/www.springerlink.com\/content\/85055g4h55622j19\/","journal-title":"J.\u00a0Sci. Comput."},{"issue":"2","key":"9366_CR12","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.cam.2006.08.029","volume":"206","author":"Y. Epshteyn","year":"2007","unstructured":"Epshteyn, Y., Rivi\u00e8re, B.: Estimation of penalty parameters for symmetric interior penalty Galerkin methods. J.\u00a0Comput. Appl. Math. 206(2), 843\u2013872 (2007)","journal-title":"J.\u00a0Comput. Appl. Math."},{"key":"9366_CR13","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4355-5","volume-title":"Theory and Practise of Finite Elements","author":"A. Ern","year":"2004","unstructured":"Ern, A., Guermond, J.-L.: Theory and Practise of Finite Elements. Applied Mathematical Sciences, vol.\u00a0159. Springer, New York (2004)"},{"issue":"1","key":"9366_CR14","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1006\/jcph.2002.7118","volume":"181","author":"J.S. Hesthaven","year":"2002","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal high-order methods on unstructured grids. I. Time-domain solution of Maxwell\u2019s equations. J.\u00a0Comput. Phys. 181(1), 186\u2013221 (2002)","journal-title":"J.\u00a0Comput. Phys."},{"issue":"1816","key":"9366_CR15","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1098\/rsta.2003.1332","volume":"362","author":"J.S. Hesthaven","year":"2004","unstructured":"Hesthaven, J.S., Warburton, T.: High-order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem. Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Eng. Sci. 362(1816), 493\u2013524 (2004)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Eng. Sci."},{"key":"9366_CR16","series-title":"Texts in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-72067-8","volume-title":"Nodal Discontinuous Galerkin Methods","author":"J.S. Hesthaven","year":"2008","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods. Texts in Applied Mathematics, vol.\u00a054. Springer, New York (2008). Algorithms, analysis, and applications"},{"key":"9366_CR17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1017\/S0962492902000041","volume":"11","author":"R. Hiptmair","year":"2002","unstructured":"Hiptmair, R.: Finite elements in computational electromagnetism. Acta Numer. 11, 237\u2013339 (2002)","journal-title":"Acta Numer."},{"issue":"3","key":"9366_CR18","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s00211-005-0604-7","volume":"100","author":"P. Houston","year":"2005","unstructured":"Houston, P., Perugia, I., Schneebeli, A., Sch\u00f6tzau, D.: Interior penalty method for the indefinite time-harmonic Maxwell equations. Numer. Math. 100(3), 485\u2013518 (2005)","journal-title":"Numer. Math."},{"issue":"1","key":"9366_CR19","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1137\/S003614290241790X","volume":"42","author":"P. Houston","year":"2004","unstructured":"Houston, P., Perugia, I., Sch\u00f6tzau, D.: Mixed discontinuous Galerkin approximation of the Maxwell operator. SIAM J. Numer. Anal. 42(1), 434\u2013459 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"9366_CR20","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10915-004-4142-8","volume":"22\/23","author":"P. Houston","year":"2005","unstructured":"Houston, P., Perugia, I., Sch\u00f6tzau, D.: Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. J.\u00a0Sci. Comput. 22\/23, 315\u2013346 (2005)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9366_CR21","series-title":"Numerical Mathematics and Scientific Computation","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198508885.001.0001","volume-title":"Finite Element Methods for Maxwell\u2019s Equations","author":"P. Monk","year":"2003","unstructured":"Monk, P.: Finite Element Methods for Maxwell\u2019s Equations. Numerical Mathematics and Scientific Computation. Oxford University Press, New York (2003)"},{"issue":"3","key":"9366_CR22","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01396415","volume":"35","author":"J.-C. N\u00e9d\u00e9lec","year":"1980","unstructured":"N\u00e9d\u00e9lec, J.-C.: Mixed finite elements in R 3. Numer. Math. 35(3), 315\u2013341 (1980)","journal-title":"Numer. Math."},{"issue":"1","key":"9366_CR23","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01389668","volume":"50","author":"J.-C. N\u00e9d\u00e9lec","year":"1986","unstructured":"N\u00e9d\u00e9lec, J.-C.: A new family of mixed finite elements in R 3. Numer. Math. 50(1), 57\u201381 (1986)","journal-title":"Numer. Math."},{"issue":"4","key":"9366_CR24","doi-asserted-by":"crossref","DOI":"10.1145\/1268776.1268778","volume":"33","author":"L. Pesch","year":"2007","unstructured":"Pesch, L., Bell, A., Sollie, H., Ambati, V.R., Bokhove, O., Van\u00a0Der Vegt, J.J.W.: hpGEM\u2014a software framework for discontinuous Galerkin finite element methods. ACM Trans. Math. Softw. 33(4), 23, 25 (2007)","journal-title":"ACM Trans. Math. Softw."},{"issue":"10","key":"9366_CR25","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1142\/S0218202503002970","volume":"13","author":"D. Sch\u00f6tzau","year":"2003","unstructured":"Sch\u00f6tzau, D., Schwab, C., Toselli, A.: Stabilized hp-DGFEM for incompressible flow. Math. Models Methods Appl. Sci. 13(10), 1413\u20131436 (2003)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"2","key":"9366_CR26","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.jcp.2004.11.017","volume":"205","author":"K. Shahbazi","year":"2005","unstructured":"Shahbazi, K.: An explicit expression for the penalty parameter of the interior penalty method. J.\u00a0Comput. Phys. 205(2), 401\u2013407 (2005)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9366_CR27","series-title":"Studies in Advanced Mathematics","volume-title":"Higher-Order Finite Element Methods","author":"P. \u0160ol\u00edn","year":"2004","unstructured":"\u0160ol\u00edn, P., Segeth, K., Dole\u017eel, I.: Higher-Order Finite Element Methods. Studies in Advanced Mathematics. Chapman & Hall\/CRC, Boca Raton (2004)"},{"key":"9366_CR28","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s10915-004-4149-1","volume":"22\/23","author":"J.J.W. Vegt van\u00a0der","year":"2005","unstructured":"van\u00a0der Vegt, J.J.W., Tomar, S.K.: Discontinuous Galerkin method for linear free-surface gravity waves. J.\u00a0Sci. Comput. 22\/23, 531\u2013567 (2005)","journal-title":"J.\u00a0Sci. Comput."},{"issue":"25\u201328","key":"9366_CR29","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1016\/j.cma.2005.06.011","volume":"195","author":"T. Warburton","year":"2006","unstructured":"Warburton, T., Embree, M.: The role of the penalty in the local discontinuous Galerkin method for Maxwell\u2019s eigenvalue problem. Comput. Methods Appl. Mech. Eng. 195(25\u201328), 3205\u20133223 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"25","key":"9366_CR30","doi-asserted-by":"crossref","first-page":"2765","DOI":"10.1016\/S0045-7825(03)00294-9","volume":"192","author":"T. Warburton","year":"2003","unstructured":"Warburton, T., Hesthaven, J.S.: On the constants in hp-finite element trace inverse inequalities. Comput. Methods Appl. Mech. Eng. 192(25), 2765\u20132773 (2003)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9366_CR31","doi-asserted-by":"crossref","DOI":"10.1515\/9781400877577","volume-title":"Geometric integration theory","author":"H. Whitney","year":"1957","unstructured":"Whitney, H.: Geometric integration theory. Princeton University Press, Princeton (1957)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-010-9366-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,28]],"date-time":"2019-02-28T07:15:26Z","timestamp":1551338126000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-010-9366-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,24]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["9366"],"URL":"https:\/\/doi.org\/10.1007\/s10915-010-9366-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4,24]]}}}