In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by extension and reduction maps, generates a fourth complex with cohomology isomorphic to the former three. This construction is used to devise new serendipity versions of rot-rot and Stokes complexes derived in the Discrete de Rham spirit.

翻译：本文致力于寻找具有增强正则性的近似de Rham复形的Serendipity版本。研究起点是一个具有普适性的新抽象构造：给定三个通过延拓映射与约化映射相互关联的复形，该构造可生成第四个复形，其同调与前三者同构。基于此构造，我们以离散de Rham方法为指导思想，推导出旋度-旋度复形与Stokes复形的新型Serendipity版本。