Pressure projection stabilized finite element method for Stokes problem with nonlinear slip boundary conditions

Li, Yuan; Li, Kaitai

doi:10.1016/j.cam.2011.02.027

Cited by 12 publications

(11 citation statements)

References 13 publications

(24 reference statements)

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“…This is done in the following proposition. Proposition 3.6 Under the hypotheses of Theorem 1.2, we have that u | Ω 0 = u 0 and p | Ω 0 = p 0 , where (u 0 , p 0 , λ 0 ) is solution of (13)- (15) with d = (0, 0) and u and p are the weak limits in (23) and (24).…”

Section: Passing To the Limit D →mentioning

confidence: 96%

“…is the solution of (13)- (15) for the corresponding d. This is done in the next section, where a priori estimates independent of d are obtained. From these estimates follows the existence of weak limits of each sequence (up to a subsequence).…”

Section: F Is a Continuous Operatormentioning

confidence: 99%

“…Using the extension operators E d and Q d and the inf-sup condition we can prove the following proposition. (13)- (15). Let…”

Section: A Priori Estimatesmentioning

confidence: 99%

“…In [2] is stated the equivalence between the mixed variational formulation (13)- (15) and the variational inequality formulation proposed in [10]. Therefore, using Theorem 3.1 p. 62 and Lemma A.1 p. 68 in [10], if (u d , p d , λ d ) is a solution www.zamm-journal.org of the mixed variational formulation (13)- (15) then (u d , p d ) is a weak solution of the Stokes problem with friction type boundary condition. So that, in the distribution sense, the couple (ξv d , ξq d ) satisfies…”

Section: Passing To the Limit D →mentioning

confidence: 99%

“…From the numerical analysis point of view, in [1,2], the authors studied the error of an inf-sup stable finite element approximation. In [15], the authors studied the error analysis of a stabilized finite element approximation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Existence result for a fluid structure interaction problem with friction type slip boundary condition

Baffico

Sassi

2014

Z Angew Math Mech

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Key words Fluid-solid interaction, variational inequality, existence result.We study the stationary interaction between a 2D viscous fluid, governed by the Stokes equation, and a rigid structure that can move following rigid displacements. The displacements of the structure are determined using an algebraic equation. A slip boundary condition of friction type is used on the fluid-solid interface. An existence result is proved and numerical tests are presented.

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Section: Passing To the Limit D →mentioning

confidence: 96%

Section: F Is a Continuous Operatormentioning

confidence: 99%

“…Using the extension operators E d and Q d and the inf-sup condition we can prove the following proposition. (13)- (15). Let…”

Section: A Priori Estimatesmentioning

confidence: 99%

Section: Passing To the Limit D →mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Existence result for a fluid structure interaction problem with friction type slip boundary condition

Baffico

Sassi

2014

Z Angew Math Mech

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Stabilised finite element method for Stokes problem with nonlinear slip condition

Gustafsson,

Videman

2024

Bit Numer Math

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This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier representing boundary traction and the stabilised formulation is based on simultaneously stabilising both the pressure and the traction. We establish the stability and the a priori error analyses, and perform a numerical convergence study in order to verify the theory.

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Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

et al. 2019

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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 P 1 -bubble element for the velocity field, P 1 element for the pressure field and the P 1 element for the Lagrange multipliers λ n and λ t defined on the slip boundary. The multiplier λ t is introduced to regularize the non-differentiable problem, whereas λ 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.

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Pressure projection stabilized finite element method for Stokes problem with nonlinear slip boundary conditions

Cited by 12 publications

References 13 publications

Existence result for a fluid structure interaction problem with friction type slip boundary condition

Existence result for a fluid structure interaction problem with friction type slip boundary condition

Stabilised finite element method for Stokes problem with nonlinear slip condition

Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

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