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Published on: September 23, 2021
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Serendipity discrete complexes with enhanced regularity
Daniele A Di Pietro1, Marien Hanot2, Marwa Salah1
1IMAG, Univ Montpellier, CNRS, Montpellier, France.
Calcolo
|October 20, 2025
Summary
Researchers developed a new abstract construction to create serendipity versions of approximate de Rham complexes. This method enhances regularity and generates novel rot-rot and Stokes complexes for advanced mathematical applications.
Area of Science:
- Mathematics
- Differential Geometry
- Complex Analysis
Background:
- Approximate de Rham complexes are crucial in various mathematical fields.
- Enhanced regularity in these complexes is a significant challenge.
- Serendipity methods offer novel approaches to complex construction.
Purpose of the Study:
- To introduce a general abstract construction for generating new complexes.
- To create serendipity versions of approximate de Rham complexes with enhanced regularity.
- To devise new rot-rot and Stokes complexes within the Discrete de Rham framework.
Main Methods:
- A novel abstract construction is presented, linking three complexes via extension and reduction maps.
- This construction generates a fourth complex with isomorphic cohomology.
- The method is applied to derive specific serendipity complexes.
Main Results:
- A new general method for constructing complexes with specific cohomology properties is established.
- Novel serendipity versions of rot-rot and Stokes complexes are successfully derived.
- The enhanced regularity of the generated complexes is demonstrated.
Conclusions:
- The abstract construction provides a powerful tool for developing new mathematical complexes.
- The devised serendipity complexes offer enhanced regularity and novel properties.
- This work advances the understanding and application of Discrete de Rham complexes.
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