What question did this study set out to answer?

February 5, 2026Open Access

Discrete Poincaré and trace inequalities for the hybridizable discontinuous Galerkin method

Key Points

The central aim is to derive discrete Poincaré and trace inequalities for the hybridizable discontinuous Galerkin method to aid stability analysis.
Deriving inequalities using the Crouzeix-Raviart space
Connecting classical discrete functional tools with HDG methods
Analyzing finite element spaces of piecewise polynomial functions
Custom-tailored inequalities enhance stability for HDG discretizations
Established well-posedness of HDG numerical schemes
Demonstrated robustness even with minimal regularity on source terms and boundaries

Abstract

Abstract In this paper, we derive discrete Poincaré and trace inequalities for the hybridizable discontinuous Galerkin (HDG) method. We employ the Crouzeix-Raviart space as a bridge, connecting classical discrete functional tools from Brenner’s foundational work (Brenner, S.C.: SIAM J. Numer. Anal. 41 (1), 306–324 (2003)) with hybridizable finite element spaces comprised of piecewise polynomial functions defined both within the element interiors and on the mesh skeleton. This approach yields custom-tailored inequalities that underpin the stability analysis of HDG discretizations. The resulting framework is then used to demonstrate the well-posedness and robustness of HDG-based numerical schemes for second-order elliptic problems, even under minimal regularity assumptions on the source term and boundary data.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Yukun Yue (Mon,) studied this question.

synapsesocial.com/papers/698434cff1d9ada3c1fb360d https://doi.org/https://doi.org/10.1007/s10543-025-01105-5

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bookmark

View Full Paper