An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method : Projections, Estimates, Tools

This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method. Front Matter ....Pages i-x Getting Ready (Shukai Du, Francisco-Javier Sayas)....Pages 1-5 Projection Analysis of Mixed Methods (Shukai Du, Francisco-Javier Sayas)....Pages 7-44 The Hybridizable Discontinuous Galerkin Method (Shukai Du, Francisco-Javier Sayas)....Pages 45-67 Variants of the HDG Method (Shukai Du, Francisco-Javier Sayas)....Pages 69-84 HDG Methods for Evolutionary Equations (Shukai Du, Francisco-Javier Sayas)....Pages 85-112 Further Reading (Shukai Du, Francisco-Javier Sayas)....Pages 113-114 Back Matter ....Pages 115-124