{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:55:50Z","timestamp":1776790550510,"version":"3.51.2"},"reference-count":61,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2010,2,20]],"date-time":"2010-02-20T00:00:00Z","timestamp":1266624000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we consider two error estimators for one-body contact problems. The first error estimator is defined in terms of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H left-parenthesis div right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mtext>div<\/mml:mtext>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">H(\\text {div})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -conforming stress approximations and equilibrated fluxes while the second is a standard edge-based residual error estimator without any modification with respect to the contact. We show reliability and efficiency for both estimators. Moreover, the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order. The second estimator is used in a control-based AFEM refinement strategy, and the decay of the error in the energy is shown. Several numerical tests demonstrate the performance of both estimators.\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02235-2","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1237-1267","source":"Crossref","is-referenced-by-count":35,"title":["A posteriori error estimator and error control for contact problems"],"prefix":"10.1090","volume":"78","author":[{"given":"Alexander","family":"Weiss","sequence":"first","affiliation":[]},{"given":"Barbara","family":"Wohlmuth","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,20]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"2320","DOI":"10.1137\/S0036142903425112","article-title":"Robust a posteriori error estimation for nonconforming finite element approximation","volume":"42","author":"Ainsworth, Mark","year":"2005","journal-title":"SIAM J. Numer. 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