Superconvergent HDG methods for Maxwell’s equations via the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e7234" altimg="si5.svg"><mml:mi>M</mml:mi></mml:math>-decomposition

The concept of the M-decomposition was introduced by Cockburn et al. (2017) to provide criteria guarantee optimal convergence rates for Hybridizable Discontinuous Galerkin (HDG) method coercive elliptic problems. In that paper they systematically constructed superconvergent hybridizable discontinuous methods approximate solutions PDEs on unstructured meshes. this paper, we use construct HDG Maxwell’s equations meshes in two dimension. particular, show any choice spaces having an M-decomposition, together with sufficiently rich auxiliary spaces, has error estimate and superconvergence even though problem is not general coercive. Motivated case, obtain a rate curl flux solution, confirmed our numerical experiments.