In this paper, a modified nonlinear Uzawa algorithm for solving symmetric saddle point problems is proposed, and also the convergence rate is analyzed. The results of numerical experiments are presented when we apply the algorithm to Stokes equations discretized by mixed finite elements. [ABSTRACT FROM AUTHOR]
Abstract: In this paper, we analyze the convergence and optimal complexity of the usual simple adaptive nonconforming finite element method by using Dörfler collective marking strategy. Based on several basic ingredients, such as the estimator reduction, quasi-orthogonality, local upper bound and so on, we eventually show the convergence of the adaptive algorithm by establishing the reduction of some total error and the quasi-optimal convergence rate. Our analysis does not need the relation between the nonconforming element and the mixed Raviart–Thomas element. The results of numerical experiments confirm that our adaptive algorithm is optimal. [Copyright &y& Elsevier]