## A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems.(English)Zbl 1198.65193

Summary: We identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree $$k\geq0$$ for both the potential as well as the flux, the order of convergence in $$L^2$$ of both unknowns is $$k+1$$. Moreover, both the approximate potential as well as its numerical trace superconverge in $$L^2$$-like norms, to suitably chosen projections of the potential, with order $$k+2$$. This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order $$k+2$$ in $$L^2$$. The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.

### MSC:

 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35L65 Hyperbolic conservation laws
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### References:

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