Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
Numerical Analysis
2013-09-17 v1
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.
Cite
@article{arxiv.1309.3608,
title = {Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem},
author = {Jun Hu and Jinchao Xu},
journal= {arXiv preprint arXiv:1309.3608},
year = {2013}
}