Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 16, Issue 1, Pages 33-68Publisher
SPRINGER
DOI: 10.1007/s10208-014-9236-6
Keywords
Adaptive finite element method; Maximum marking; Instance optimality; Newest vertex bisection
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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 square root of the squared energy error plus the squared oscillation. This result will be derived in the model setting of Poisson's equation on a polygon, linear finite elements, and conforming triangulations created by newest vertex bisection.
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