{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T20:57:39Z","timestamp":1758315459957,"version":"3.44.0"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s00211-025-01479-2","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T07:23:38Z","timestamp":1755588218000},"page":"1259-1284","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The unique continuation problem for the wave equation discretized with a high-order space-time nonconforming method"],"prefix":"10.1007","volume":"157","author":[{"given":"Erik","family":"Burman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillaume","family":"Delay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandre","family":"Ern","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"issue":"5","key":"1479_CR1","doi-asserted-by":"publisher","first-page":"1024","DOI":"10.1137\/0330055","volume":"30","author":"C Bardos","year":"1992","unstructured":"Bardos, C., Lebeau, G., Rauch, J.: Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control. Optim. 30(5), 1024\u20131065 (1992)","journal-title":"SIAM J. Control. Optim."},{"issue":"4","key":"1479_CR2","doi-asserted-by":"publisher","first-page":"983","DOI":"10.2140\/apde.2017.10.983","volume":"10","author":"J Le Rousseau","year":"2017","unstructured":"Le Rousseau, J., Lebeau, G., Terpolilli, P., Tr\u00e9lat, E.: Geometric control condition for the wave equation with a time-dependent observation domain. Anal. PDE 10(4), 983\u20131015 (2017)","journal-title":"Anal. PDE"},{"issue":"7","key":"1479_CR3","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/S0764-4442(97)80053-5","volume":"325","author":"N Burq","year":"1997","unstructured":"Burq, N., G\u00e9rard, P.: Condition n\u00e9cessaire et suffisante pour la contr\u00f4labilit\u00e9 exacte des ondes. C. R. Acad. Sci. Paris S\u00e9r. I Math. 325(7), 749\u2013752 (1997)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"issue":"4","key":"1479_CR4","doi-asserted-by":"publisher","first-page":"971","DOI":"10.3934\/ipi.2015.9.971","volume":"9","author":"E B\u00e9cache","year":"2015","unstructured":"B\u00e9cache, E., Bourgeois, L., Franceschini, L., Dard\u00e9, J.: Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case. Inverse Probl. Imaging 9(4), 971\u20131002 (2015)","journal-title":"Inverse Probl. Imaging"},{"key":"1479_CR5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/31\/7\/075001","author":"N C\u00eendea","year":"2015","unstructured":"C\u00eendea, N., M\u00fcnch, A.: Inverse problems for linear hyperbolic equations using mixed formulations. Inver. Prob. (2015). https:\/\/doi.org\/10.1088\/0266-5611\/31\/7\/075001","journal-title":"Inver. Prob."},{"issue":"2","key":"1479_CR6","doi-asserted-by":"publisher","first-page":"998","DOI":"10.1137\/20M1315798","volume":"59","author":"L Baudouin","year":"2021","unstructured":"Baudouin, L., Buhan, M., Ervedoza, S., Osses, A.: Carleman-based reconstruction algorithm for waves. SIAM J. Numer. Anal. 59(2), 998\u20131039 (2021)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"1479_CR7","doi-asserted-by":"publisher","first-page":"2227","DOI":"10.1051\/m2an\/2023050","volume":"57","author":"W Dahmen","year":"2023","unstructured":"Dahmen, W., Monsuur, H., Stevenson, R.: Least squares solvers for ill-posed PDEs that are conditionally stable. ESAIM Math. Model. Numer. Anal. 57(4), 2227\u20132255 (2023)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"3","key":"1479_CR8","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s10092-014-0116-x","volume":"52","author":"N C\u00eendea","year":"2015","unstructured":"C\u00eendea, N., M\u00fcnch, A.: A mixed formulation for the direct approximation of the control of minimal L2-norm for linear type wave equations. Calcolo 52(3), 245\u2013288 (2015)","journal-title":"Calcolo"},{"issue":"3","key":"1479_CR9","doi-asserted-by":"publisher","first-page":"1519","DOI":"10.1137\/19M1249424","volume":"58","author":"E Burman","year":"2020","unstructured":"Burman, E., Feizmohammadi, A., Oksanen, L.: A fully discrete numerical control method for the wave equation. SIAM J. Control. Optim. 58(3), 1519\u20131546 (2020)","journal-title":"SIAM J. Control. Optim."},{"key":"1479_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1051\/cocv\/2023028","volume":"29","author":"E Burman","year":"2023","unstructured":"Burman, E., Feizmohammadi, A., M\u00fcnch, A., Oksanen, L.: Spacetime finite element methods for control problems subject to the wave equation. ESAIM Control Optim. Calc. Var. 29, 41\u201340 (2023)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"1479_CR11","doi-asserted-by":"crossref","unstructured":"Ervedoza, S., Zuazua, E.: Numerical Approximation of Exact Controls for Waves. SpringerBriefs in Mathematics, p. 122. Springer, New-York (2013)","DOI":"10.1007\/978-1-4614-5808-1"},{"issue":"6","key":"1479_CR12","doi-asserted-by":"publisher","first-page":"2752","DOI":"10.1137\/130916862","volume":"35","author":"E Burman","year":"2013","unstructured":"Burman, E.: Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput. 35(6), 2752\u20132780 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"7\u20138","key":"1479_CR13","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1016\/j.crma.2014.06.008","volume":"352","author":"E Burman","year":"2014","unstructured":"Burman, E.: Error estimates for stabilized finite element methods applied to ill-posed problems. C. R. Math. Acad. Sci. Paris 352(7\u20138), 655\u2013659 (2014)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"311","key":"1479_CR14","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1090\/mcom\/3255","volume":"87","author":"E Burman","year":"2018","unstructured":"Burman, E., Hansbo, P.: Stabilized nonconforming finite element methods for data assimilation in incompressible flows. Math. Comp. 87(311), 1029\u20131050 (2018)","journal-title":"Math. Comp."},{"issue":"129","key":"1479_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.matpur.2018.10.003","volume":"9","author":"E Burman","year":"2019","unstructured":"Burman, E., Nechita, M., Oksanen, L.: Unique continuation for the Helmholtz equation using stabilized finite element methods. J. Math. Pures Appl. 9(129), 1\u201322 (2019)","journal-title":"J. Math. Pures Appl."},{"issue":"5","key":"1479_CR16","doi-asserted-by":"publisher","first-page":"2368","DOI":"10.1137\/20M1375619","volume":"59","author":"E Burman","year":"2021","unstructured":"Burman, E., Delay, G., Ern, A.: A hybridized high-order method for unique continuation subject to the Helmholtz equation. SIAM J. Numer. Anal. 59(5), 2368\u20132392 (2021)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1479_CR17","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/s00211-018-0949-3","volume":"139","author":"E Burman","year":"2018","unstructured":"Burman, E., Oksanen, L.: Data assimilation for the heat equation using stabilized finite element methods. Numer. Math. 139(3), 505\u2013528 (2018)","journal-title":"Numer. Math."},{"issue":"5","key":"1479_CR18","doi-asserted-by":"publisher","first-page":"2065","DOI":"10.1051\/m2an\/2018030","volume":"52","author":"E Burman","year":"2018","unstructured":"Burman, E., Ish-Horowicz, J., Oksanen, L.: Fully discrete finite element data assimilation method for the heat equation. ESAIM Math. Model. Numer. Anal. 52(5), 2065\u20132082 (2018)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"5","key":"1479_CR19","doi-asserted-by":"publisher","first-page":"2534","DOI":"10.1137\/22M1508637","volume":"61","author":"E Burman","year":"2023","unstructured":"Burman, E., Delay, G., Ern, A.: The unique continuation problem for the heat equation discretized with a high-order space-time nonconforming method. SIAM J. Numer. Anal. 61(5), 2534\u20132557 (2023)","journal-title":"SIAM J. Numer. Anal."},{"issue":"324","key":"1479_CR20","doi-asserted-by":"publisher","first-page":"1681","DOI":"10.1090\/mcom\/3508","volume":"89","author":"E Burman","year":"2020","unstructured":"Burman, E., Feizmohammadi, A., Oksanen, L.: A finite element data assimilation method for the wave equation. Math. Comp. 89(324), 1681\u20131709 (2020)","journal-title":"Math. Comp."},{"key":"1479_CR21","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1051\/m2an\/2020062","volume":"55(suppl.)","author":"E Burman","year":"2021","unstructured":"Burman, E., Feizmohammadi, A., M\u00fcnch, A., Oksanen, L.: Space time stabilized finite element methods for a unique continuation problem subject to the wave equation. ESAIM Math. Model. Numer. Anal. 55(suppl.), 969\u2013991 (2021)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"1479_CR22","doi-asserted-by":"publisher","unstructured":"Burman, E., Preuss, J.: Unique continuation for the wave equation based on a discontinuous Galerkin time discretization. preprint (2024). IMA Journal of Numerical Analysis, 2025; draf036, https:\/\/doi.org\/10.1093\/imanum\/draf036","DOI":"10.1093\/imanum\/draf036"},{"issue":"2","key":"1479_CR23","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1137\/19M1285901","volume":"43","author":"E Burman","year":"2021","unstructured":"Burman, E., Cicuttin, M., Delay, G., Ern, A.: An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. SIAM J. Sci. Comput. 43(2), 859\u2013882 (2021)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"1479_CR24","doi-asserted-by":"publisher","first-page":"2374","DOI":"10.1137\/S0036142902405217","volume":"41","author":"OA Karakashian","year":"2003","unstructured":"Karakashian, O.A., Pascal, F.: A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal. 41(6), 2374\u20132399 (2003)","journal-title":"SIAM J. Numer. Anal."},{"issue":"259","key":"1479_CR25","doi-asserted-by":"publisher","first-page":"1119","DOI":"10.1090\/S0025-5718-07-01951-5","volume":"76","author":"E Burman","year":"2007","unstructured":"Burman, E., Ern, A.: Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comp. 76(259), 1119\u20131140 (2007)","journal-title":"Math. Comp."},{"issue":"4","key":"1479_CR26","doi-asserted-by":"publisher","first-page":"1367","DOI":"10.1051\/m2an\/2016066","volume":"51","author":"A Ern","year":"2017","unstructured":"Ern, A., Guermond, J.-L.: Finite element quasi-interpolation and best approximation. ESAIM Math. Model. Numer. Anal. 51(4), 1367\u20131385 (2017)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"1","key":"1479_CR27","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1142\/S0218202507001826","volume":"17","author":"P Houston","year":"2007","unstructured":"Houston, P., Sch\u00f6tzau, D., Wihler, T.P.: Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems. Math. Models Methods Appl. Sci. 17(1), 33\u201362 (2007)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"1479_CR28","volume-title":"Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming","author":"M Cicuttin","year":"2017","unstructured":"Cicuttin, M., Di Pietro, D.A., Ern, A.: Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. J. Comput. Appl, Math (2017)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01479-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-025-01479-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01479-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T16:30:39Z","timestamp":1758299439000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-025-01479-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["1479"],"URL":"https:\/\/doi.org\/10.1007\/s00211-025-01479-2","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"type":"print","value":"0029-599X"},{"type":"electronic","value":"0945-3245"}],"subject":[],"published":{"date-parts":[[2025,8]]},"assertion":[{"value":"19 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 August 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}