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Comp."],"abstract":"<p>\n                    In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu [Found. Comput. Math. 21 (2021), pp.\u00a01739\u20131774]. This paper extends their approach to three-dimensional finite element complexes. The finite element Hessian, elasticity, and divdiv complexes are systematically derived by applying techniques such as smooth finite element de Rham complexes, the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"t\">\n                        <mml:semantics>\n                          <mml:mi>t<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">t<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -\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                    decomposition, and trace complexes, along with related two-dimensional finite element analogs. The construction includes two reduction operations and one augmentation operation to address continuity differences in the BGG diagram, ultimately resulting in a comprehensive and effective framework for constructing finite element complexes, which have various applications in PDE solving.\n                  <\/p>","DOI":"10.1090\/mcom\/4079","type":"journal-article","created":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T13:32:27Z","timestamp":1739453547000},"page":"1083-1142","source":"Crossref","is-referenced-by-count":0,"title":["Complexes from complexes: Finite element complexes in three dimensions"],"prefix":"10.1090","volume":"95","author":[{"given":"Long","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuehai","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-3-030-33116-0_2","article-title":"The incompatibility operator: from Riemann\u2019s intrinsic view of geometry to a new model of elasto-plasticity","author":"Amstutz, Samuel","year":"[2019] \\copyright2019","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030331153"},{"key":"2","doi-asserted-by":"crossref","unstructured":"J. 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