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math.NA2013★ 32 cited
Instance optimality of the adaptive maximum strategy
Lars Diening, Christian Kreuzer, Rob Stevenson
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of…
math.NA2013★ 14 cited
Convex Hull Property and Maximum Principle for Finite Element Minimisers of General Convex Functionals
Lars Diening, Christian Kreuzer, Sebastian Schwarzacher
The convex hull property is the natural generalization of maximum principles from scalar to vector valued functions. Maximum principles for finite element approximations are often…