Error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems
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In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form 𝒪(1/h^1+δ), where h denotes the mesh size and δ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity and boundedness (with h^δ-dependency), and we derive updated error estimates for both discrete energy- and L^2-norms. All theoretical results are supported by numerical evidence.
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