Titlebook: An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method; Projections, Estimat Shukai‘Du,Francisco-Javier Sayas Book 2

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Sara Gerke,Jochen Taupitz,Heiko Zimmermanncheme as the classical HDG method. This method involves a projection in the numerical flux, an idea that can be traced back to the work of Lehrenfeld and Sch?berl [87]. In the following table, we compare the spaces for the hybridizable formulations of RT and BDM with HDG and the new variant of HDG that we will be discussing.

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Sara Gerke,Jochen Taupitz,Heiko Zimmermannholtz, heat, and wave equations, but the applications of HDG go much further into nonlinear, vector-valued, or non-selfadjoint equations. In this very short chapter, we will give some hints at “classics” or relevant recent contributions to the analysis and practice of HDG methods.

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Getting Ready,ties in a reference configuration. They belong to the category of what the FEM community calls .. We will not be using anything specific from FEM theory, but the arguments will be familiar to anyone aware of these techniques.

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Projection Analysis of Mixed Methods,Thomas space. Their original and very often quoted paper [109] contains a two-dimensional finite element for the . space, which is slightly different from the one that is now known as the RT space. The three-dimensional space is one of the many elements that appears in the first of the two big finit

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The Hybridizable Discontinuous Galerkin Method,stabilization (not penalization) function. This is how local quantities of RT, BDM, and HDG methods compare. Note that there is no natural finite element structure for ., where we can recognize boundary and internal degrees of freedom. Instead, we will have a projection that integrates . into the sa