{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:49:30Z","timestamp":1777610970458,"version":"3.51.4"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"281","license":[{"start":{"date-parts":[[2013,6,6]],"date-time":"2013-06-06T00:00:00Z","timestamp":1370476800000},"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 propose a class of new tailored finite point methods (TFPM) for the numerical solution of a type of convection-diffusion-reaction problems in two dimensions. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. We also study the error estimates of our TFPM. We prove that our TFPM can achieve good accuracy even when the mesh size\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h much-greater-than epsilon\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo>\n                              \u226b\n                              \n                            <\/mml:mo>\n                            <mml:mi>\n                              \u03b5\n                              \n                            <\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">h\\gg \\varepsilon<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for some cases without any prior knowledge of the boundary layers. Our numerical examples show the efficiency and reliability of our method.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02616-0","type":"journal-article","created":{"date-parts":[[2012,6,6]],"date-time":"2012-06-06T10:48:37Z","timestamp":1338979717000},"page":"213-226","source":"Crossref","is-referenced-by-count":27,"title":["Tailored finite point method based on exponential bases for convection-diffusion-reaction equation"],"prefix":"10.1090","volume":"82","author":[{"given":"Houde","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongyi","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,6,6]]},"reference":[{"key":"1","unstructured":"M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, National Bureau of Standards, 1964."},{"issue":"166","key":"2","doi-asserted-by":"publisher","first-page":"465","DOI":"10.2307\/2007596","article-title":"A priori estimates and analysis of a numerical method for a turning point problem","volume":"42","author":"Berger, Alan E.","year":"1984","journal-title":"Math. 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Media","ISSN":"https:\/\/id.crossref.org\/issn\/1556-1801","issn-type":"print"},{"key":"12","first-page":"237","article-title":"A difference scheme for a differential equation with a small parameter multiplying the highest derivative","volume":"6","author":"Il\u2032in, A. M.","year":"1969","journal-title":"Mat. Zametki","ISSN":"https:\/\/id.crossref.org\/issn\/0025-567X","issn-type":"print"},{"issue":"5","key":"13","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.aml.2006.08.001","article-title":"Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem","volume":"20","author":"Kellogg, R. Bruce","year":"2007","journal-title":"Appl. Math. 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Theory Methods Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1004-8979","issn-type":"print"},{"key":"23","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1017\/S0962492904000261","article-title":"Steady-state convection-diffusion problems","volume":"14","author":"Stynes, Martin","year":"2005","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2013-82-281\/S0025-5718-2012-02616-0\/S0025-5718-2012-02616-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2013-82-281\/S0025-5718-2012-02616-0\/S0025-5718-2012-02616-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:24:54Z","timestamp":1776792294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2013-82-281\/S0025-5718-2012-02616-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,6]]},"references-count":23,"journal-issue":{"issue":"281","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["S0025-5718-2012-02616-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2012-02616-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2012,6,6]]}}}