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We study the convergence of an adaptive Interior Penalty Discontinuous Galerkin (IPDG) method for a 2D model second order elliptic boundary value problem. Based on a residual-type a posteriori error estimator, we prove that after each refinement step of the adaptive scheme we achieve a guaranteed reduction of the global discretization error in the mesh… (More)

A method is proposed to determine the modal spectra of waves supported by arrays, which are composed of multiple rows of scatterers randomly disordered around an underlying periodic configuration. The method is applied to the canonical problem of arrays of identical small acoustically-soft circular cylinders, and disorder in the location of the rows. Two… (More)

In the context of periodic homogenization based on the periodic unfolding method, we extend the existing convergence results for the boundary periodic unfolding operator to gradients defined on manifolds. These general results are then used to homogenize a system of five coupled reaction–diffusion equations, three of which are defined on a manifold. The… (More)

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