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Explore the intricacies of convergence theory for adaptive finite element methods (AFEM) in this comprehensive lecture. Delve into the detailed proof of AFEM convergence when applied to elliptic partial differential equations. Learn about approximation classes and discover how AFEMs achieve the best possible convergence rate. Presented as part of the Hausdorff Trimester Program Multiscale Problems: Winter School on Numerical Analysis of Multiscale Problems, this 1-hour 23-minute talk offers valuable insights for researchers and students in numerical analysis and computational mathematics.
