{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:27:44Z","timestamp":1776868064641,"version":"3.51.2"},"reference-count":26,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CRC 1173"],"award-info":[{"award-number":["CRC 1173"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We establish an abstract space-time DPG framework for the\napproximation of linear waves in heterogeneous media. The estimates\nare based on a suitable variational setting in the energy space. The\nanalysis combines the approaches for acoustic waves of Gopalakrishnan\u2013Sepulveda [J. Gopalakrishnan and P. Sepulveda,\nA space-time DPG method for the wave equation in multiple dimensions,\nSpace-Time Methods. Applications to Partial Differential Equations,\nRadon Ser. Comput. Appl. Math. 21,\nWalter de Gruyter, Berlin 2019, 129\u2013154]\nand Ernesti\u2013Wieners [J. Ernesti and C. Wieners,\nA space-time discontinuous Petrov\u2013Galerkin method for acoustic waves,\nSpace-Time Methods. Applications to Partial Differential Equations,\nRadon Ser. Comput. Appl. Math. 21,\nWalter de Gruyter, Berlin 2019, 99\u2013127]\nand is based on the abstract definition of traces on the skeleton of\nthe time-space substructuring. The method is evaluated by large-scale\nparallel computations motivated from applications in seismic imaging,\nwhere the computational domain can be restricted substantially to a subset\nof the full space-time cylinder.<\/jats:p>","DOI":"10.1515\/cmam-2018-0190","type":"journal-article","created":{"date-parts":[[2019,4,9]],"date-time":"2019-04-09T16:56:03Z","timestamp":1554828963000},"page":"465-481","source":"Crossref","is-referenced-by-count":22,"title":["Space-Time Discontinuous Petrov\u2013Galerkin Methods for Linear Wave Equations in Heterogeneous Media"],"prefix":"10.1515","volume":"19","author":[{"given":"Johannes","family":"Ernesti","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Angewandte und Numerische Mathematik , KIT , Karlsruhe , Germany"}]},{"given":"Christian","family":"Wieners","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Angewandte und Numerische Mathematik , KIT , Karlsruhe , Germany"}]}],"member":"374","published-online":{"date-parts":[[2019,4,9]]},"reference":[{"key":"2023033110340726452_j_cmam-2018-0190_ref_001_w2aab3b7d750b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"K. D.  Blazek, C.  Stolk and W. W.  Symes,\nA mathematical framework for inverse wave problems in heterogeneous media,\nInverse Problems 29 (2013), no. 6, Article ID 065001.","DOI":"10.1088\/0266-5611\/29\/6\/065001"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_002_w2aab3b7d750b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"D.  Braess,\nFinite Elements. Theory, Fast Solvers, and Applications in Elasticity Theory, 3rd ed.,\nCambridge University, Cambridge, 2007.","DOI":"10.1017\/CBO9780511618635"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_003_w2aab3b7d750b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"F.  Brezzi and M.  Fortin,\nMixed and Hybrid Finite Element Methods,\nSpringer Ser. Comput. Math. 15,\nSpringer, New York, 1991.","DOI":"10.1007\/978-1-4612-3172-1"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_004_w2aab3b7d750b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"D.  Broersen, W.  Dahmen and R. P.  Stevenson,\nOn the stability of DPG formulations of transport equations,\nMath. Comp. 87 (2018), no. 311, 1051\u20131082.","DOI":"10.1090\/mcom\/3242"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_005_w2aab3b7d750b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"A.  Brougois, M.  Bourget, P.  Lailly, M.  Poulet, P.  Ricarte and R.  Versteeg,\nMarmousi, model and data,\nEAEG Workshop \u2013 Practical Aspects of Seismic Data Inversion,\nEuropean Association of Geoscientists & Engineers, Copenhagen (1990), 1\u201312.","DOI":"10.3997\/2214-4609.201411190"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_006_w2aab3b7d750b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, L.  Demkowicz and J.  Gopalakrishnan,\nBreaking spaces and forms for the DPG method and applications including Maxwell equations,\nComput. Math. Appl. 72 (2016), no. 3, 494\u2013522.","DOI":"10.1016\/j.camwa.2016.05.004"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_007_w2aab3b7d750b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and F.  Hellwig,\nLow-order discontinuous Petrov\u2013Galerkin finite element methods for linear elasticity,\nSIAM J. Numer. Anal. 54 (2016), no. 6, 3388\u20133410.","DOI":"10.1137\/15M1032582"},{"key":"2023033110340726452_j_cmam-2018-0190_ref_008_w2aab3b7d750b1b6b1ab2ab8Aa","unstructured":"R.  Dautray and J.-L.  Lions,\nMathematical Analysis and Numerical Methods for Science and Technology. Vol. 5: Evolution Problems. I,\nSpringer, Berlin, 1992."},{"key":"2023033110340726452_j_cmam-2018-0190_ref_009_w2aab3b7d750b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"L. F.  Demkowicz and J.  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