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We show the existence of a evolving displacement field in H\u00f6lder space with H\u00f6lder exponent $\\gamma \\in (0,1]$. The rate of convergence of the finite difference approximation depends on the factor $C_s h^\\gamma\/\\epsilon^2$ where $\\epsilon$ gives the length scale of nonlocal interaction, $h$ is the discretization length, and $C_s$ is the maximum of H\u00f6lder norm of the solution and its second derivatives during the evolution. It is shown that the rate of convergence holds for both the forward Euler scheme as well as general single step implicit schemes. A stability result is established for the semidiscrete approximation. The H\u00f6lder continuous evolutions are seen to converge to a brittle fracture evolution in the limit of vanishing nonlocality.<\/jats:p>","DOI":"10.1137\/17m1112236","type":"journal-article","created":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T12:20:36Z","timestamp":1523362836000},"page":"906-941","source":"Crossref","is-referenced-by-count":21,"title":["Numerical Analysis of Nonlocal Fracture Models in H\u00f6lder Space"],"prefix":"10.1137","volume":"56","author":[{"given":"Prashant K.","family":"Jha","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Lipton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,10]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s10704-011-9628-4"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2010.519136"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.01.027"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050051"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/PL00004617"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10704-012-9725-z"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2439"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2010.10.014"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2006.04.001"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2013.07.022"},{"key":"atypb11","volume-title":"Lecture Notes","author":"Driver B. 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