# Serendipity discrete complexes with enhanced regularity

## TL;DR

The paper introduces a new method to construct discrete complexes with improved regularity for mathematical modeling.

## Contribution

A novel abstract construction generates a fourth complex with cohomology isomorphic to three given complexes.

## Key findings

- A general framework is introduced for creating serendipity versions of discrete complexes.
- New serendipity rot–rot and Stokes complexes are derived using the Discrete de Rham approach.

## Abstract

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.