{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:49:42Z","timestamp":1776836982429,"version":"3.51.2"},"reference-count":53,"publisher":"American Mathematical Society (AMS)","issue":"343","license":[{"start":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T00:00:00Z","timestamp":1711065600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are quasi constant-free and apply to a large class of variational problems including the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Dirichlet problem, as well as degenerate minimization, obstacle and image de-noising problems. In addition, these a posteriori error estimates are based on a comparison to a given non-conforming finite element solution. For the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -Dirichlet problem, these a posteriori error bounds are equivalent to residual type a posteriori error bounds and, hence, reliable and efficient.\n                  <\/p>","DOI":"10.1090\/mcom\/3821","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T15:08:08Z","timestamp":1672844888000},"page":"2247-2279","source":"Crossref","is-referenced-by-count":13,"title":["Explicit and efficient error estimation for convex minimization problems"],"prefix":"10.1090","volume":"92","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[]},{"given":"Alex","family":"Kaltenbach","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,3,22]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics (New York)","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824","volume-title":"A posteriori error estimation in finite element analysis","author":"Ainsworth, Mark","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/047129411X"},{"key":"2","doi-asserted-by":"crossref","unstructured":"A. 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