Instance optimality of the adaptive maximum strategy
arXiv:1306.0377
Originality Incremental advance
AI Analysis
Provides theoretical justification for a widely used adaptive method in computational PDEs, though limited to a specific model setting.
Proved that the adaptive finite element method with maximum marking strategy achieves instance optimality for total error in solving Poisson's equation on polygons with linear finite elements.
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 the energy error and the 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.