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• W3015356166 abstract "In this paper, we study superconvergence properties of the ultraweak-local discontinuous Galerkin (UWLDG) method in Tao et al. [To appear in Math. Comput. DOI: https://doi.org/10.1090/mcom/3562 (2020).] for an one-dimensional linear fourth-order equation. With special initial discretizations, we prove the numerical solution of the semi-discrete UWLDG scheme superconverges to a special projection of the exact solution. The order of this superconvergence is proved to be k + min(3, k ) when piecewise ℙ k polynomials with k ≥ 2 are used. We also prove a 2 k -th order superconvergence rate for the cell averages and for the function values and derivatives of the UWLDG approximation at cell boundaries. Moreover, we prove superconvergence of ( k + 2)-th and ( k + 1)-th order of the function values and the first order derivatives of the UWLDG solution at a class of special quadrature points, respectively. Our proof is valid for arbitrary non-uniform regular meshes and for arbitrary k ≥ 2. Numerical experiments verify that all theoretical findings are sharp." @default.
• W3015356166 created "2020-04-17" @default.
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• W3015356166 date "2020-07-31" @default.
• W3015356166 modified "2023-10-16" @default.
• W3015356166 title "Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation" @default.
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• W3015356166 doi "https://doi.org/10.1051/m2an/2020023" @default.
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