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Stokes equation under Tresca friction boundary condition: a truncated approach

Abstract : In this paper, we discuss the convergence of the finite element solution of the Stokes equations under slip boundary condition of friction type. The weak formulation of this problem is a variational inequality of second type for which it is documented that when finite element approximation is used for its approximation, the interpolation error on the slip zone is the main factor driven the reduced convergence rate observed.The approach in this work is different.The starting point is the introduction of a truncated (cut off) function, followed by the formulation of a truncated problem which is thoroughly analysed in its continuous and discrete formulation. We show linear convergence rate of the finite element solution by assuming standard regularity of the weak solution. This improves all previous results. Numerical experiments exhibited are in agreement with the theoretical findings provide a suitable choice of the truncation parameter.
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https://hal.archives-ouvertes.fr/hal-03323588
Contributor : Djoko Kamdem Connect in order to contact the contributor
Submitted on : Sunday, August 22, 2021 - 7:59:47 AM
Last modification on : Wednesday, August 25, 2021 - 3:31:10 AM

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  • HAL Id : hal-03323588, version 1

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Jules Djoko, Jonas Koko, Sognia Konlack. Stokes equation under Tresca friction boundary condition: a truncated approach. [Research Report] African Peer Review Mechanism. 2021. ⟨hal-03323588⟩

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