Abstract
We analyse the adaptive finite-element approximation to solutions
of partial differential equations in variational formulation. Assuming
well-posedness of the continuous problem and requiring only basic
properties of the adaptive algorithm, we prove convergence of the
sequence of discrete solutions to the true one. The proof is based
on the ideas by Morin, Siebert and Veeser but replaces local efficiency
of the estimator by a local density property of the adaptively generated
finite-element spaces. As a result, estimators without a discrete
lower bound are also included in our theory. The assumptions of the
presented framework are fulfilled by a large class of important applications,
estimators and adaptive strategies.
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