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Conditions for superconvergence of HDG methods for second-order elliptic problems. (English) Zbl 1251.65158

The authors provide a projection-based analysis of a large class of finite element methods for second order elliptic problems. They obtain sufficient conditions for the optimal convergence of the approximate flux and the superconvergence of an element-by-element postprocessing of the scalar variable. A template for constructing the hybridizable discontinuous Galerkin (HDG) method is also proposed.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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