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• W2953238618 abstract "Classical inf-sup stable mixed finite elements for the incompressible (Navier-)Stokes equations are not pressure-robust, i.e., their velocity errors depend on the continuous pressure. However, a modification only in the right hand side of a Stokes discretization is able to reestablish pressure-robustness, as shown recently for several inf-sup stable Stokes elements with discontinuous discrete pressures. In this contribution, this idea is extended to low and high order Taylor-Hood and mini elements, which have continuous discrete pressures. For the modification of the right hand side a velocity reconstruction operator is constructed that maps discretely divergence-free test functions to exactly divergence-free ones. The reconstruction is based on local $H(mathrm{div})$-conforming flux equilibration on vertex patches, and fulfills certain orthogonality properties to provide consistency and optimal a-priori error estimates. Numerical examples for the incompressible Stokes and Navier-Stokes equations confirm that the new pressure-robust Taylor-Hood and mini elements converge with optimal order and outperform significantly the classical versions of those elements when the continuous pressure is comparably large." @default.
• W2953238618 created "2019-06-27" @default.
• W2953238618 creator A5021823634 @default.
• W2953238618 creator A5024764407 @default.
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• W2953238618 date "2016-09-13" @default.
• W2953238618 modified "2023-09-23" @default.
• W2953238618 title "Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations With Continuous Pressure Finite Elements" @default.
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• W2953238618 hasPublicationYear "2016" @default.
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