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Locally refined meshes, however, dictate a small time step everywhere with a crippling effect on any explicit time-marching method. In [J. Diaz and M. J. Grote, SIAM J. Sci. Comput., 31 (2009), pp. 1985--2014] a leap-frog (LF)-based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time steps in the locally refined region and larger steps elsewhere. Here optimal convergence rates are rigorously proved for the fully discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.<\/jats:p>","DOI":"10.1137\/17m1121925","type":"journal-article","created":{"date-parts":[[2018,4,17]],"date-time":"2018-04-17T14:23:54Z","timestamp":1523975034000},"page":"994-1021","source":"Crossref","is-referenced-by-count":11,"title":["Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation"],"prefix":"10.1137","volume":"56","author":[{"given":"Marcus J.","family":"Grote","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michaela","family":"Mehlin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan A.","family":"Sauter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384162"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0732037"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0713048"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2004.02.023"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90073-1"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30726-6"},{"key":"atypb8","volume-title":"North-Holland","author":"Ciarlet P.","year":"1987"},{"key":"atypb9","volume-title":"Spectral\/HP Element for CFD","author":"Karniadakis G.","year":"2005"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997329554"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0447-4"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0447-4"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.03.035"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-007-9151-y"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-008-9235-3"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.01.018"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-012-9669-5"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/070709414"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2015.03.027"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.09.038"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.2007.03427.x"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/0710073"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1997.1412"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934907"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/140958293"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.04.028"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.09.046"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/05063194X"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-011-0332-6"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/15M1038037"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09017-6"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/040603437"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.02.021"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65161-8"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-007-9128-x"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1190\/geo2012-0252.1"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.03.032"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1142\/S0218396X0100067X"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.01.002"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1002\/mma.3355"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2006035"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.11.012"},{"key":"atypb43","unstructured":"T. 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