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The convergence of an adaptive mixed finite element method for general secondorder linear elliptic problems defined on simply connected bounded polygonaldomains is analyzed in this paper. The main difficulties in the analysis areposed by the non-symmetric and indefinite form of the problem along with thelack of the orthogonality property in mixed finite element methods. Theimportant tools in the analysis are a posteriori error estimators,quasi-orthogonality property and quasi-discrete reliability established usingrepresentation formula for the lowest-order Raviart-Thomas solution in terms ofthe Crouzeix-Raviart solution of the problem. An adaptive marking in each stepfor the local refinement is based on the edge residual and volume residualterms of the a posteriori estimator. Numerical experiments confirm thetheoretical analysis.

Convergence of an adaptive mixed finite element method for general second order linear elliptic problems