A unified error analysis of HDG methods for the static Maxwell equations
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We propose a framework that allows us to analyze different variants of HDG methods for the static Maxwell equations using one simple analysis. It reduces all the work to the construction of projections that best fit the structures of the approximation spaces. As applications, we analyze four variants of HDG methods (denoted by B, H, B+, H+), where two of them are known (variants H, B+) and the other two are new (variants H+, B). We show that all the four variants are optimally convergent and that variants B+ and H+ achieve superconvergence without post-processing. For the two known variants, we prove their optimal convergence under weaker requirements of the meshes and the stabilization functions thanks to the new analysis techniques being introduced. At the end, we provide numerical experiments to support the analysis.
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