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- W2963064249 abstract "In this article, we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use |$H(textrm{div})$|-conforming finite elements, as they provide major benefits such as exact mass conservation and pressure-independent error estimates. The main aspect of this work lies in the analysis of high-order approximations. We show that the considered method is uniformly stable with respect to the polynomial order |$k$| and provides optimal error estimates |$| {textbf{u} - textbf{u}_h} |_{1_h} + | {{it {Pi}}^{Q_h} p-p_h} |_{0} le c left(h/k right)^s | textbf{u} |_{s+1} $|. To derive these estimates, we prove a |$k$|-robust Ladyženskaja-Babuška-Brezzi (LBB) condition. This proof is based on a polynomial |$H^2$|-stable extension operator. This extension operator itself is of interest for the numerical analysis of |$C^0$|-continuous discontinuous Galerkin methods for fourth-order problems." @default.
- W2963064249 created "2019-07-30" @default.
- W2963064249 creator A5021823634 @default.
- W2963064249 creator A5057077776 @default.
- W2963064249 date "2017-08-29" @default.
- W2963064249 modified "2023-09-23" @default.
- W2963064249 title "Polynomial robust stability analysis for $H$(div)-conforming finite elements for the Stokes equations" @default.
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- W2963064249 doi "https://doi.org/10.1093/imanum/drx051" @default.
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