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Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids. (English) Zbl 1326.65147
The authors consider the discontinuous Galerkin method applied to the Poisson equation. Some a posteriori error estimates are derived. The results hold in a setting in which a variable polynomial degree and simplicial meshes with hanging nodes are allowed. An approach allowing for simple (nonconforming) flux reconstructions is proposed. An algebraic error flux reconstruction is introduced. Guaranteed reliability and local efficiency are proved and an adaptive strategy combining both adaptive mesh refinement and adaptive stopping criteria is proposed. Numerical experiments illustrate a tight control of the overall error, good prediction of the distribution of the discretization and algebraic error components, and efficiency of the adaptive strategy.

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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