Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs

July 14, 17:30 ~ 17:55

Near-Best Approximation on Adaptive Partitions

Peter Binev

University of South Carolina, United States   -   binev@math.sc.edu

We consider adaptive approximation of a function on a given domain $\Omega$ using piecewise polynomial functions. To study this approximation, the partitioning of $\Omega$ is related to building a binary tree $T$ whose leaves represent the elements of the partition. The problem of approximating a function is presented then as the process of identifying a tree $T$ and the related approximating polynomials $P(\Delta)$ for each of its leaves $\Delta$. We consider two cases of adaptivity: the h-adaptivity in which the polynomials $P(\Delta)$ are of the same order and the hp-adaptivity in which the orders of $P(\Delta)$ may vary for different $\Delta$-s. We use error functionals to drive the adaptive process and prove that the presented algorithms provide a near-best approximation in both cases.

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