Convergence and Optimal Complexity of Adaptive Finite Element Methods. (arXiv:1002.0887v1 [math.NA])

In this paper, we study adaptive finite element approximations in a
perturbation framework, which makes use of the existing adaptive finite element
analysis of a linear symmetric elliptic problem. We prove the convergence and
complexity of adaptive finite element methods for a class of elliptic partial
differential equations. For illustration, we apply the general approach to
obtain the convergence and complexity of adaptive finite element methods for a
nonsymmetric problem, a nonlinear problem as well as an unbounded coefficient
eigenvalue problem.

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Original source : http://arxiv.org/abs/1002.0887...