An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method by Shukai Du & Francisco-Javier Sayas

Author:Shukai Du & Francisco-Javier Sayas
Language: eng
Format: epub
ISBN: 9783030272302
Publisher: Springer International Publishing

For , we consider the spaces

(4.1)

and the subspace decomposition . Note how the polynomial degree for is one order higher, which makes this method resemble a traditional Finite Element scheme, and quite the opposite of a BDM method (where is the higher order space). The stabilization function now is of the form

where the last condition can be written as the existence of two positive constants such that

A final ingredient of the method is the orthogonal projection

that we have used for theoretical purposes in past sections. This projection will be a key ingredient for the method. The new numerical flux is

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