1. Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation
- Author
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Mekki Ayadi, Leonardo Baffico, Hela Ayed, Taoufik Sassi, Université de Sousse, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
- Subjects
Numerical Analysis ,Applied Mathematics ,Mathematical analysis ,General Engineering ,Slip (materials science) ,Lambda ,01 natural sciences ,Finite element method ,Theoretical Computer Science ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,Computational Theory and Mathematics ,Lagrange multiplier ,Stokes problem ,symbols ,Vector field ,Uniqueness ,Boundary value problem ,0101 mathematics ,Software ,ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,Mathematics - Abstract
In this work, a finite element approximation of the Stokes problem under a slip boundary condition of friction type, known as the Tresca boundary condition, is considered. We treat the approximate problem of a four field mixed formulation using the $${\mathbb {P}}^{1}$$ -bubble element for the velocity field, $${\mathbb {P}}^{1}$$ element for the pressure field and the $${\mathbb {P}}^{1}$$ element for the Lagrange multipliers $$\lambda _{n}$$ and $$\lambda _{t}$$ defined on the slip boundary. The multiplier $$\lambda _{t}$$ is introduced to regularize the non-differentiable problem, whereas $$\lambda _{n}$$ treats the impermeability condition. Existence and uniqueness results for both continuous and discrete problems are proven and an a priori error estimate is established. Numerical realization of such problem is discussed and some numerical tests are provided.
- Published
- 2019