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Optimal adaptive nonconforming FEM for the Stokes problem

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Abstract

This paper presents an optimal nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the Stokes equations with respect to natural approximation classes. The proof does not explicitly involve the pressure variable and follows from a novel discrete Helmholtz decomposition of deviatoric functions.

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Correspondence to Daniel Peterseim.

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Carsten Carstensen was supported by the World Class University (WCU) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology R31-2008-000-10049-0. Daniel Peterseim was supported by the DFG research center Matheon ‘Mathematics in the key technologies’. Hella Rabus was supported by the DFG research group 797 ‘Analysis and Computation of Microstructure in Finite Plasticity’.

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Carstensen, C., Peterseim, D. & Rabus, H. Optimal adaptive nonconforming FEM for the Stokes problem. Numer. Math. 123, 291–308 (2013). https://doi.org/10.1007/s00211-012-0490-8

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  • DOI: https://doi.org/10.1007/s00211-012-0490-8

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