{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T16:52:45Z","timestamp":1777999965260,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The dynamic contact problem describing collision of an elastic bar with a rigid obstacle, prescribed by an initial velocity, is considered in a variational formulation. The non-smooth, piecewise-linear solution is constructed analytically using partition of a 2D rectangular domain along characteristics. Challenged by the discontinuous velocity after collision, full discretization of the problem is applied that is based on a space-time finite element method. For an iterative solution of the discrete variational inequality, a primal\u2013dual active set algorithm is used. Computer simulation of the collision problem is presented on uniform triangle grids. The active sets defined in the 2D space-time domain converge in a few iterations after re-initialization. The benchmark solution at grid points is indistinguishable from the analytical solution. The discrete energy has no dissipation, it is free of spurious oscillations, and it converges super-linearly under mesh refinement.<\/jats:p>","DOI":"10.3390\/computation13090210","type":"journal-article","created":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T14:02:46Z","timestamp":1756735366000},"page":"210","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Space-Time Primal-Dual Active Set Method: Benchmark for Collision of Elastic Bar with Discontinuous Velocity"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5664-2625","authenticated-orcid":false,"given":"Victor A.","family":"Kovtunenko","sequence":"first","affiliation":[{"name":"Department of Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstr. 36, 8010 Graz, Austria"},{"name":"Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, 630090 Novosibirsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1119\/1.2733680","article-title":"Falling elastic bars and springs","volume":"75","author":"Aguirregabiria","year":"2007","journal-title":"Am. 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