{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:36:12Z","timestamp":1776800172679,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,7,13]],"date-time":"2016-07-13T00:00:00Z","timestamp":1468368000000},"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                    Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm. Numerical results are given to illustrate the theoretical error bounds.\n                  <\/p>","DOI":"10.1090\/mcom\/2998","type":"journal-article","created":{"date-parts":[[2015,7,13]],"date-time":"2015-07-13T11:15:16Z","timestamp":1436786116000},"page":"581-599","source":"Crossref","is-referenced-by-count":13,"title":["Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type"],"prefix":"10.1090","volume":"85","author":[{"given":"J.","family":"Gracia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"O\u2019Riordan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,7,13]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"918","DOI":"10.1023\/A:1021103512850","article-title":"Pointwise and weighted a priori estimates for the solution and its first derivative of a singularly perturbed convection-diffusion equation","volume":"38","author":"Andreev, V. 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