P1

Long Chen, Michael Holst, and Jinchao Xu. Convergence and Optimality of Adaptive Mixed Finite Element Methods.

under revision

ABSTRACT: The convergence and optimality of adaptive mixed finite element methods for second order elliptic partial differential equations is established in this paper. The main difficulty for the mixed finite element method is the lack of minimization principle and thus the failure of orthogonality. A quasi-orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace, while the part of the error containing divergence can be bounded by data oscillation.