{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:42:29Z","timestamp":1787330549792,"version":"build-2736575974"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this article we describe applications of the numerical method of discrete differential forms in computational general relativity (GR). In particular, we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As described in an earlier paper, the discrete differential form approach provides accurate results in spherically symmetric static space-times [R. Richter, J. Frauendiener, and M. Vogel, Classical Quantum Gravity, 24 (2007), p. 433], and it is manifestly coordinate independent. Here, we extend the method to time dependent systems. We use the polarized Gowdy solution as a testbed for two numerical schemes. One scheme reproduces that solution very well; in particular, it is stable for a long time and converges quadratically.<\/jats:p>","DOI":"10.1137\/080734583","type":"journal-article","created":{"date-parts":[[2010,4,14]],"date-time":"2010-04-14T18:13:19Z","timestamp":1271268799000},"page":"1140-1158","source":"Crossref","is-referenced-by-count":3,"title":["Discrete Differential Forms for $(1+1)$-Dimensional Cosmological Space-Times"],"prefix":"10.1137","volume":"32","author":[{"given":"Ronny","family":"Richter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Frauendiener","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,4,14]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/2\/019"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"T.W. Baumgarte and S.L. Shapiro,\n                      Numerical relativity and compact binaries\n                      , Phys. Rep. 376 (2003), pp. 41\u2013131.","DOI":"10.1016\/S0370-1573(02)00537-9"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"B.K. Berger,\n                      Numerical approaches to spacetime singularities\n                      , Living Rev. Relativity, 5 (2002), http:\/\/www.livingreviews.org\/lrr-2002-1.","DOI":"10.12942\/lrr-2002-1"},{"key":"R4","unstructured":"A. Bossavit,\n                      Computational Electromagnetism\n                      , Academic Press, Boston, 1998."},{"key":"R5","unstructured":"A. Bossavit,\n                      Mixed finite elements and the complex of Whitney forms\n                      , in The Mathematics of Finite Elements and Applications VI, J. Whiteman, ed., Academic Press, London, 1988, pp. 137\u2013144."},{"key":"R6","unstructured":"A. Bossavit,\n                      Discretization of Electromagnetic Problems\n                      , Technical report, Interdyscyplinary Centre for Mathematical and Computational Modelling, Warsaw, 1998\u20132000, http:\/\/www.icm.edu.pl\/edukacja\/mat\/DEP.php."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"\u00c9. Cartan,\n                      Riemannian Geometry in an Orthogonal Frame\n                      , World Scientific, Singapore, 2001.","DOI":"10.1142\/4808"},{"key":"R8","unstructured":"T. Frankel,\n                      The Geometry of Physics\u2014An Introduction\n                      , Cambridge University Press, Cambridge, 1997."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/23\/16\/S05"},{"key":"R10","unstructured":"M. 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Munkres,\n                      Simplicial complexes and simplicial maps\n                      , in Elements of Algebraic Topology, chap. 1.2., Perseus Press, New York, 1993, pp. 7\u201314."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396415"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.58.064022"},{"key":"R21","unstructured":"M.J.D. Powell,\n                      A hybrid method for nonlinear equations\n                      , in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon and Breach, New York, 1970."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.55.4705"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"P.A. Raviart and J.M. Thomas,\n                      A mixed finite element method for 2nd order elliptic problems\n                      , in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, I. Galligani and E. 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Pulverer, eds., Chapman and Hall, Boca Raton, 2001, pp. 179\u2013187."},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/15\/004"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080734583","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:11:48Z","timestamp":1787328708000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080734583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080734583"],"URL":"https:\/\/doi.org\/10.1137\/080734583","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}