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摘要
This paper provides a refined a posteriori error control for the obstacle problem with an affine obstacle which allows for a proof of optimal complexity of an adaptive algorithm. This is the first adaptive mesh-refining finite element method known to be of optimal complexity for some variational inequality. The result holds for first-order conforming finite element methods in any spacial dimension based on shape-regular triangulation into simplices for an affine obstacle. The key contribution is the discrete reliability of the a posteriori error estimator from [6] in an edge-oriented modification which circumvents the difficulties caused by the non-existence of a positive second-order approximation [18].
- 出版日期2015-7
- 单位北京大学
