{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:50:33Z","timestamp":1776844233863,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"240","license":[{"start":{"date-parts":[[2002,11,20]],"date-time":"2002-11-20T00:00:00Z","timestamp":1037750400000},"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                    We consider finite element operators defined on \u201crough\u201d functions in a bounded polyhedron\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"normal\">\n                            \u03a9\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R Superscript upper N\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}^N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"normal\">\n                            \u03a9\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"normal\">\n                            \u03a9\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01369-2","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T14:12:48Z","timestamp":1032531168000},"page":"1405-1419","source":"Crossref","is-referenced-by-count":29,"title":["Positivity preserving finite element approximation"],"prefix":"10.1090","volume":"71","author":[{"given":"Ricardo","family":"Nochetto","sequence":"first","affiliation":[]},{"given":"Lars","family":"Wahlbin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,11,20]]},"reference":[{"key":"1","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387941932"},{"key":"2","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and hybrid finite element methods","volume":"15","author":"Brezzi, Franco","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0387975829"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s002110050009","article-title":"Residual type a posteriori error estimates for elliptic obstacle problems","volume":"84","author":"Chen, Zhiming","year":"2000","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"4","doi-asserted-by":"crossref","unstructured":"P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, Vol II (Finite Element Methods (Part 1)), P.G. Ciarlet and J.L. Lions eds, North-Holland, 1991, 17-351.","DOI":"10.1016\/S1570-8659(05)80039-0"},{"key":"5","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1051\/m2an\/197509R200771","article-title":"Approximation by finite element functions using local regularization","volume":"9","author":"Cl\u00e9ment, Ph.","year":"1975","journal-title":"Rev. Fran\\c{c}aise Automat. Informat. Recherche Op\\'{e}rationnelle S\\'{e}r. Rouge Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0397-9342","issn-type":"print"},{"key":"6","doi-asserted-by":"publisher","first-page":"81","DOI":"10.2307\/2005248","article-title":"A mollifier useful for approximations in Sobolev spaces and some applications to approximating solutions of differential equations","volume":"27","author":"Hilbert, Stephen","year":"1973","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"7","series-title":"Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. III","volume-title":"Linear operators and approximation theory","author":"Korovkin, P. P.","year":"1960"},{"key":"8","volume-title":"Approximation of functions","author":"Lorentz, G. G.","year":"1966"},{"key":"9","unstructured":"R. H. Nochetto, K. Siebert, and A. Veeser, Pointwise a posteriori error control of elliptic obstacle problems (to appear)."},{"issue":"190","key":"10","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2307\/2008497","article-title":"Finite element interpolation of nonsmooth functions satisfying boundary conditions","volume":"54","author":"Scott, L. Ridgway","year":"1990","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"11","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/BF01395933","article-title":"Approximation in the finite element method","volume":"19","author":"Strang, Gilbert","year":"1972","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"12","unstructured":"R. Verf\u00fcrth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, 1996."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01369-2\/S0025-5718-01-01369-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01369-2\/S0025-5718-01-01369-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:03:58Z","timestamp":1776726238000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-240\/S0025-5718-01-01369-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,20]]},"references-count":12,"journal-issue":{"issue":"240","published-print":{"date-parts":[[2002,10]]}},"alternative-id":["S0025-5718-01-01369-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01369-2","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":[[2001,11,20]]}}}