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arXiv · 1309.3608

Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem

Jun Hu·Jinchao Xu
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Abstract

In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in this saddle point problem, we introduce a new prolongation operator to carry through the discrete reliability analysis for the error estimator. We then use a specially defined interpolation operator to prove that, up to oscillation, the error can be bounded by the approximation error within a properly defined nonlinear approximate class. Finally, by introducing a new parameter-dependent error estimator, we prove the convergence and optimality estimates.

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Jun Hu, Jinchao Xu. 2013-09-13. Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem. https://arxiv.org/abs/1309.3608

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