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Volume 11, Issue 1
On the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Condition

J. K. Djoko

Int. J. Numer. Anal. Mod., 11 (2014), pp. 34-53.

Published online: 2014-11

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  • Abstract

This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretized in time based on backward Euler's scheme. We prove existence and uniqueness of the solution of the time discrete problem by means of a regularization approach. Finally, we derive error estimates that justify the convergence property of the discretization proposed.

  • Keywords

Stokes equations, slip boundary condition, variational inequality, regularization, convexity, monotone.

  • AMS Subject Headings

65M12, 76D07, 35J85, 35Q30, 76D30, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-34, author = {Djoko , J. K.}, title = {On the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Condition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {1}, pages = {34--53}, abstract = {

This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretized in time based on backward Euler's scheme. We prove existence and uniqueness of the solution of the time discrete problem by means of a regularization approach. Finally, we derive error estimates that justify the convergence property of the discretization proposed.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/513.html} }
TY - JOUR T1 - On the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Condition AU - Djoko , J. K. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 34 EP - 53 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/513.html KW - Stokes equations, slip boundary condition, variational inequality, regularization, convexity, monotone. AB -

This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretized in time based on backward Euler's scheme. We prove existence and uniqueness of the solution of the time discrete problem by means of a regularization approach. Finally, we derive error estimates that justify the convergence property of the discretization proposed.

Djoko , J. K.. (2014). On the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Condition. International Journal of Numerical Analysis and Modeling. 11 (1). 34-53. doi:
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