On the numerical solution of the stationary power-law Stokes equations : a penalty nite element approach

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Authors

Djoko, J.K. (Jules Kamdem)
Lubuma, Jean M.-S.
Mbehou, M.

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Springer

Abstract

In this work, we study the penalty finite element approximation of the stationary power law Stokes problem. We prove uniform convergence of the finite element solution with respect to the penalized parameter under classical assumptions on the weak solution. We formulate and analyze the convergence of a nonlinear saddle point problem by adopting a particular algorithm based on vanishing viscosity approach and long time behavior of an initial value problem. Finally, the predictions observed theoretically are validated by means of numerical experiments.

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Keywords

Power-law Stokes equations, Penalty finite element method, Uniform convergence, Algorithm, Initial value problem, Initial flow

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Citation

Djoko, J.K., Lubuma, J.M. & Mbehou, M. On the numerical solution of the stationary power-law Stokes equations : a penalty nite element approach. Journal of Scientific Computing (2016) 69: 1058-1082. doi:10.1007/s10915-016-0227-4.