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• W2963865949 abstract "Abstract We propose stress formulation of the Stokes equations. The velocity $u$ is approximated with $H(operatorname{div})$-conforming finite elements providing exact mass conservation. While many standard methods use $H^1$-conforming spaces for the discrete velocity $H(operatorname{div})$-conformity fits the considered variational formulation in this work. A new stress-like variable $sigma $ equalling the gradient of the velocity is set within a new function space $H(operatorname{curl} operatorname{div})$. New matrix-valued finite elements having continuous ‘normal-tangential’ components are constructed to approximate functions in $H(operatorname{curl} operatorname{div})$. An error analysis concludes with optimal rates of convergence for errors in $u$ (measured in a discrete $H^1$-norm), errors in $sigma $ (measured in $L^2$) and the pressure $p$ (also measured in $L^2$). The exact mass conservation property is directly related to another structure-preservation property called pressure robustness, as shown by pressure-independent velocity error estimates. The computational cost measured in terms of interface degrees of freedom is comparable to old and new Stokes discretizations." @default.
• W2963865949 created "2019-07-30" @default.
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• W2963865949 date "2019-05-17" @default.
• W2963865949 modified "2023-09-30" @default.
• W2963865949 title "A mass conserving mixed stress formulation for the Stokes equations" @default.
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• W2963865949 doi "https://doi.org/10.1093/imanum/drz022" @default.
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