3 papers
math.NA2026
Mesh-Uniform Stability and Error Estimates for HDG Discretizations of the Helmholtz Equation
Yukun Yue
We revisit the hybridizable discontinuous Galerkin method of Cui and Zhang for the Helmholtz equation with first-order absorbing boundary condition. Their analysis proves stability…
math.NA2026
Stability and Convergence of HDG Schemes under Minimal Regularity
Jiannan Jiang, Noel J. Walkington, Yukun Yue
Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it…
math.NA2025
Discrete Poincaré and Trace Inequalities for the Hybridizable Discontinuous Galerkin Method
Yukun Yue
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, conne…