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An accurate \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1129.65085
Summary: We introduce a new \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. The reconstructed flux is computed elementwise and its divergence equals the \(L^{2}\)-orthogonal projection of the source term onto the discrete space. Moreover, the energy-norm of the error in the flux is bounded by the discrete energy-norm of the error in the primal variable, independently of diffusion heterogeneities.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
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