Analysis of BDDC Preconditioners for Nonconforming Polytopal Hybrid Discretization Methods

SIAM Journal on Numerical Analysis, Volume 64, Issue 2, Page 456-484, April 2026.
Abstract. In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; doi:10.1007/s10208-025-09734-6) to analyze the convergence rate of the balancing domain decomposition by constraints (BDDC) preconditioner generated from nonconforming polytopal hybrid discretizations. We prove polylogarithmic bounds on the condition number for the preconditioner that are independent of the mesh parameter and the number of subdomains and that hold on polytopal meshes. The analysis relies on the continuity of a face truncation operator, which we establish in the fully discrete polytopal setting. To validate the theory, we present numerical experiments that confirm the truncation estimate and condition number bounds. In particular, we conduct weak scalability tests for second-order elliptic problems discretized using discontinuous skeletal methods, specifically hybridizable discontinuous Galerkin and hybrid high-order methods. We also demonstrate the robustness of the preconditioner for piecewise discontinuous coefficients with large jumps.