Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems

In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using variable second-order elliptic problems. The strategy is to use penalization function the form O ( 1 / h + δ ) , where denotes mesh size and user-dependent parameter. We then quantify its direct impact on convergence analysis, namely, (strong) consistency, discrete coercivity boundedness (with -dependency), updated both energy- L 2 -norms. originality analysis relies specifically conforming interpolants exact solution. All theoretical results are supported by numerical evidence. • Families Hybridizable Interior Penalty diffusion Unified & estimates. -dependency condition boundedness. stabilization term strongly influences estimated rates robustness. Superconvergence symmetric scheme achieved κ -orthogonal grids selecting an appropriate