Geodesic
Superconvergence by M-decompositions. Part II: Construction of two-dimensional finite elements
Cockburn, Bernardo1  ; Fu, Guosheng1
1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 165-186

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We apply the concept of an M-decomposition introduced in Part I to systematically construct local spaces defining superconvergent hybridizable discontinuous Galerkin methods, and their companion sandwiching mixed methods. This is done in the framework of steady-state diffusion problems for the h- and p-versions of the methods for general polygonal meshes in two-space dimensions.

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DOI : 10.1051/m2an/2016016
Classification : 65M60, 65N30, 58J32, 65N15
Keywords: Hybridizable discontinuous Galerkin methods, superconvergence, polygonal meshes

Cockburn, Bernardo 1 ; Fu, Guosheng 1

1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. 
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Cockburn, Bernardo; Fu, Guosheng. Superconvergence by $M$-decompositions. Part II: Construction of two-dimensional finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 165-186. doi: 10.1051/m2an/2016016

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