FoCM 2014 conference

Workshop A5 - Multiresolution and Adaptivity in Numerical PDEs

December 12, 14:30 ~ 15:10 - Room B22

Near-Best hp-Adaptive Approximation

Peter Binev

University of South Carolina, United States   -

The hp-adaptive numerical methods for PDEs combine the domain decomposition with assignment of degrees of freedom at each element of a particular refinement. The main objective of this talk is to introduce a framework that streamlines the process of making adaptive decisions.

We consider domain partitioning based on a fixed binary refinement scheme and a coarse-to-fine routine for making adaptive decisions about the elements to be split and the polynomial orders to be assigned. The problem of finding near-optimal results is managed by using greedy algorithms on binary trees and a modification of the local errors that take into account the local complexity of the adaptive approximation. We prove that the algorithm provides near-best approximation to any given function.

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