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Advanced Numerical Methods in the Mathematical Sciences

Bernardo Cockburn, University of Minnesota
The Evolution of the HDG Methods: An Overview


We describe the evolution of the so-called hybridizable discontinuous Galerkin (HDG) since their inception (back in 2005) until the present day. After defining them, within the setting of steady-state diffusion, we present several ways of rewriting the methods to be able to establish links with many other numerical methods, especially with the discontinuous Galerkin methods. We then sketch the main developments of the HDG methods. We end by briefly describing the main developments of their applications to a wide variety of partial differential equations of practical interest.