We are concerned with a convergence analysis of adaptive mixed and nonconfoming finite element methods for second order elliptic boundary value problems. In case of standard conforming Lagrangian type finite element approximations, such an analysis has been initiated in [11] and has been further investigated in [6,14,15]. The methods presented in this contribution provide a guaranteed reduction of the discretization error. The analysis is carried out for a model problem and discretizations by the lowest order Raviart-Thomas and Crouzeix-Raviart finite elements. The essential steps in the convergence proof are the reliability of the estimator, a discrete local efficiency, and quasi-orthogonality properties. We do not require any regularity of the solution nor do we make use of duality arguments.
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