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• W3024247951 abstract "We introduce a new discretization for the stream function formulation of the incompressible Stokes equations in two and three space dimensions. The method is strongly related to the Hellan-Herrmann-Johnson method and is based on the recently discovered mass conserving mixed stress formulation [J. Gopalakrishnan, P.L. Lederer, J. Schoberl, IMA Journal of numerical Analysis, 2019] that approximates the velocity in an $H(operatorname{div})$-conforming space and introduces a new stress-like variable for the approximation of the gradient of the velocity within the function space $H(operatorname{curl}operatorname{div})$. The properties of the (discrete) de Rham complex allows to extend this method to a stream function formulation in two and three space dimensions. We present a detailed stability analysis in the continuous and the discrete setting where the stream function $psi$ and its approximation $psi_h$ are elements of $H(operatorname{curl})$ and the $H(operatorname{curl})$-conforming Nedelec finite element space, respectively. We conclude with an error analysis revealing optimal convergence rates for the error of the discrete velocity $u_h = operatorname{curl}(psi_h)$ measured in a discrete $H^1$-norm. We present numerical examples to validate our findings and discuss structure-preserving properties such as pressure-robustness." @default.
• W3024247951 created "2020-05-21" @default.
• W3024247951 creator A5057077776 @default.
• W3024247951 date "2020-05-13" @default.
• W3024247951 modified "2023-09-27" @default.
• W3024247951 title "A Hellan-Herrmann-Johnson-like method for the stream function formulation of the Stokes equations in two and three space dimensions" @default.
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• W3024247951 hasPublicationYear "2020" @default.
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