{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T10:04:03Z","timestamp":1778580243085,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2009,6,9]],"date-time":"2009-06-09T00:00:00Z","timestamp":1244505600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2010,10]]},"DOI":"10.1007\/s10915-009-9301-5","type":"journal-article","created":{"date-parts":[[2009,6,8]],"date-time":"2009-06-08T13:59:08Z","timestamp":1244469548000},"page":"118-150","source":"Crossref","is-referenced-by-count":64,"title":["Revisiting and Extending Interface Penalties for\u00a0Multi-domain Summation-by-Parts Operators"],"prefix":"10.1007","volume":"45","author":[{"given":"Mark H.","family":"Carpenter","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Nordstr\u00f6m","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Gottlieb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,6,9]]},"reference":[{"key":"9301_CR1","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1006\/jcph.2000.6420","volume":"160","author":"S. Abarbanel","year":"2000","unstructured":"Abarbanel, S., Chertock, A.E.: Strict stability of high-order compact difference schemes: the role of boundary conditions for hyperbolic pde\u2019s I (and II). J.\u00a0Comput. Phys. 160, 42\u201366 (2000)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9301_CR2","series-title":"Lecture Notes in Comput. Sci. Engrg.","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/978-3-642-59721-3_5","volume-title":"Discontinuous Galerkin Methods: Theory, Computation and Applications","author":"D.N. Arnold","year":"2000","unstructured":"Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Discontinuous Galerkin methods for elliptic problems. In: Cockburn, B., Karniadakis, G.E., Shu, C.-W. (eds.) Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Comput. Sci. Engrg., vol. 11, pp. 89\u2013101. Springer, New York (2000)"},{"issue":"5","key":"9301_CR3","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D.N. Arnold","year":"2002","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 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9301_CR4","first-page":"331","volume":"175","author":"C.E. Baumann","year":"1999","unstructured":"Baumann, C.E., Oden, J.T.: A discontinuous hp finite element method for the Euler and Navier-Stokes equations,\u00a0I. J. Numer. Methods Fluids 175, 331\u2013341 (1999)","journal-title":"J. Numer. Methods Fluids"},{"key":"9301_CR5","unstructured":"Carpenter, M.H., Kennedy, C.A.: Fourth-order 2n-storage Runge-Kutta schemes. NASA-TM-109111, April 1994"},{"key":"9301_CR6","doi-asserted-by":"crossref","unstructured":"Carpenter, M.H., Gottlieb, D., Abarbanel, S.: Time-stable boundary conditions for finite difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes. J.\u00a0Comput. Phys. 111(2) (1994)","DOI":"10.1006\/jcph.1994.1057"},{"key":"9301_CR7","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1006\/jcph.1996.0234","volume":"129","author":"M.H. Carpenter","year":"1996","unstructured":"Carpenter, M.H., Gottlieb, D.: Spectral methods on arbitrary grids. J. Comput. Phys. 129, 74\u201386 (1996)","journal-title":"J. Comput. Phys."},{"key":"9301_CR8","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1006\/jcph.1998.6114","volume":"148","author":"M.H. Carpenter","year":"1999","unstructured":"Carpenter, M.H., Nordstr\u00f6m, J., Gottlieb, D.: A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148, 341\u2013365 (1999)","journal-title":"J. Comput. Phys."},{"key":"9301_CR9","unstructured":"Carpenter, M.H., Nordstr\u00f6m, J., Gottlieb, D.: Revisiting and extending interface penalties for multi-domain summation-by-parts operators. NASA\/TM-2007-214892 (2007)"},{"key":"9301_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(90)90196-8","volume":"90","author":"G. Chesshire","year":"1990","unstructured":"Chesshire, G., Henshaw, W.D.: Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90, 1\u201364 (1990)","journal-title":"J. Comput. Phys."},{"key":"9301_CR11","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B. Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440\u20132463 (1998)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"9301_CR12","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1137\/0731079","volume":"31","author":"W.S. Don","year":"1994","unstructured":"Don, W.S., Gottlieb, D.: The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points. SIAM J. Numer. Anal. 31(6), 1519\u20131534 (1994)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9301_CR13","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10915-006-9123-7","volume":"32","author":"P. Diener","year":"2007","unstructured":"Diener, P., Dorband, E.N., Schnetter, E., Tiglio, M.: J. Sci. Comput. 32(1), 109\u2013145 (2007)","journal-title":"J. Sci. Comput."},{"key":"9301_CR14","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1090\/S0025-5718-1975-0386296-7","volume":"29","author":"B. Gustafsson","year":"1975","unstructured":"Gustafsson, B.: The convergence rate for difference approximations to mixed initial boundary value problems. Math. Comput. 29, 396\u2013406 (1975)","journal-title":"Math. Comput."},{"issue":"3","key":"9301_CR15","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1137\/S1064827594268488","volume":"17","author":"J.S. Hesthaven","year":"1996","unstructured":"Hesthaven, J.S., Gottlieb, D.: A stable penalty method for the compressible Navier-Stokes equations, I:\u00a0open boundary conditions. SIAM J. Sci. Comput. 17(3), 579\u2013612 (1996)","journal-title":"SIAM J. Sci. Comput."},{"key":"9301_CR16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1137\/S1064827594276540","volume":"18","author":"J.S. Hesthaven","year":"1997","unstructured":"Hesthaven, J.S.: A stable penalty method for the compressible Navier-Stokes equations,\u00a0II: one-dimensional domain decomposition schemes. SIAM J. Sci. Comput. 18, 3 (1997)","journal-title":"SIAM J. Sci. Comput."},{"key":"9301_CR17","doi-asserted-by":"crossref","first-page":"2352","DOI":"10.1137\/S1064827598343723","volume":"21","author":"J.S. Hesthaven","year":"2000","unstructured":"Hesthaven, J.S., Teng, C.H.: Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21, 2352\u20132380 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"9301_CR18","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,\u00a0I: time-domain solution of Maxwell\u2019s equations. J. Comput. Phys. 181, 186\u2013221 (2002)","journal-title":"J. Comput. Phys."},{"key":"9301_CR19","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal high-order methods on unstructured grids,\u00a0II: nonlinear problems. J.\u00a0Comput. Phys."},{"key":"9301_CR20","volume-title":"Initial-Boundary Value Problems and the Navier-Stokes Equation","author":"H.O. Kreiss","year":"1989","unstructured":"Kreiss, H.O., Lorenz, J.: Initial-Boundary Value Problems and the Navier-Stokes Equation. Academic Press, New York (1989)"},{"key":"9301_CR21","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/cpa.3160130205","volume":"13","author":"P.D. Lax","year":"1960","unstructured":"Lax, P.D., Wendroff, B.: Systems of conservation laws. Commun. Pure Appl. Math. 13, 217\u2013237 (1960)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"9301_CR22","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1023\/A:1020342429644","volume":"18","author":"K. Mattsson","year":"2003","unstructured":"Mattsson, K.: Boundary procedures for summation-by-parts operators. J. Sci. Comput. 18(1), 133\u2013153 (2003)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"9301_CR23","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1023\/B:JOMP.0000027955.75872.3f","volume":"21","author":"K. Mattsson","year":"2004","unstructured":"Mattsson, K., Sv\u00e4rd, M., Nordstr\u00f6m, J.: Stable and accurate artificial dissipation. J. Sci. Comput. 21(1), 57\u201379 (2004)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"9301_CR24","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.jcp.2004.03.001","volume":"199","author":"K. Mattsson","year":"2004","unstructured":"Mattsson, K., Nordstr\u00f6m, J.: Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199(2), 503\u2013540 (2004)","journal-title":"J. Comput. Phys."},{"key":"9301_CR25","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1006\/jcph.1998.6133","volume":"148","author":"J. Nordstr\u00f6m","year":"1999","unstructured":"Nordstr\u00f6m, J., Carpenter, M.H.: Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations. J. Comput. Phys. 148, 621\u2013645 (1999)","journal-title":"J. Comput. Phys."},{"key":"9301_CR26","unstructured":"Nordstr\u00f6m, J., Gustafsson, R.: High order finite difference approximations of electromagnetic wave propagation close to material discontinuities. J.\u00a0Sci. Comput. 18(2) (2003)"},{"key":"9301_CR27","first-page":"14","volume-title":"Proceedings of Conference in Honor of Professor H.-C. Huang on the Occasion of His Retirement","author":"C.-W. Shu","year":"2000","unstructured":"Shu, C.-W.: Different formulations of the discontinuous Galerkin method for the viscous terms. In: Xui, W.M., Shi, Z.C., Mu, M., Zou, J. (eds.) Proceedings of Conference in Honor of Professor H.-C. Huang on the Occasion of His Retirement, pp. 14\u201345. Science Press, New York (2000)"},{"issue":"1","key":"9301_CR28","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1006\/jcph.1994.1005","volume":"110","author":"B. Strand","year":"1994","unstructured":"Strand, B.: Summation by parts for finite difference approximations for d\/dx. J. Comput. Phys. 110(1), 47\u201367 (1994)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9301_CR29","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1023\/A:1025881528802","volume":"20","author":"M. Sv\u00e4rd","year":"2004","unstructured":"Sv\u00e4rd, M.: On coordinate transformations for summation-by-parts operators. J. Sci. Comput. 20(1), 29\u201342 (2004)","journal-title":"J. Sci. Comput."},{"key":"9301_CR30","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.jcp.2006.02.014","volume":"218","author":"M. Sv\u00e4rd","year":"2006","unstructured":"Sv\u00e4rd, M., Nordstr\u00f6m, J.: On the order of accuracy for difference approximations of initial-boundary value problems. J. Comput. Phys. 218, 333\u2013352 (2006)","journal-title":"J. Comput. Phys."},{"key":"9301_CR31","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1016\/j.jcp.2009.01.011","volume":"228","author":"N.K. Jamaleev","year":"2009","unstructured":"Jamaleev, N.K., Carpenter, M.H.: Third-order energy stable WENO scheme. J. Comput. Phys. 228, 3025\u20133047 (2009)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-009-9301-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-009-9301-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-009-9301-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:41:32Z","timestamp":1559464892000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-009-9301-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,9]]},"references-count":31,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["9301"],"URL":"https:\/\/doi.org\/10.1007\/s10915-009-9301-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6,9]]}}}