{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:47:05Z","timestamp":1776836825515,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"342","license":[{"start":{"date-parts":[[2024,2,2]],"date-time":"2024-02-02T00:00:00Z","timestamp":1706832000000},"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                    A classical technique to construct polynomial preserving extensions of scalar functions defined on the boundary of an\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    simplex to the interior is to use so-called rational blending functions. The purpose of this paper is to generalize the construction by blending to the de Rham complex. More precisely, we define polynomial preserving extensions which map traces of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -forms defined on the boundary of the simplex to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -forms defined in the interior. Furthermore, the extensions are cochain maps, i.e., they commute with the exterior derivative.\n                  <\/p>","DOI":"10.1090\/mcom\/3819","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T15:08:06Z","timestamp":1672844886000},"page":"1575-1594","source":"Crossref","is-referenced-by-count":1,"title":["Construction of polynomial preserving cochain extensions by blending"],"prefix":"10.1090","volume":"92","author":[{"given":"Richard","family":"Falk","sequence":"first","affiliation":[]},{"given":"Ragnar","family":"Winther","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,2,2]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1002\/mana.200610762","article-title":"Explicit polynomial preserving trace liftings on a triangle","volume":"282","author":"Ainsworth, Mark","year":"2009","journal-title":"Math. 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