Graduate Seminar "Aktuelle Themen der Numerik"


Thursday, May 08, 2014, 02:00 pm

Tree Approximation for hp-Adaptivity

Prof. Peter Binev (University of South Carolina)

The hp-adaptive approximation is formulated as an approximation problem on a full binary
tree T, where for each of the leaves ∆ an order p(∆) ≥ 1 is assigned in such a way that the
sum of all such p(∆) does not exceed N, called complexity of the approximation. The leaves
∆ correspond to the cells of the partition, while p(∆) is the order of the polynomial used
for the local approximation on ∆. Devising an incremental algorithm for near-best adaptive
approximation for the problem of finding the best possible tree T  and assignments p(∆) leads
to building a construction that attaches a ghost tree with p(∆) leaves to each leaf ∆ of T with
p(∆) > 1. The resulting full binary tree T  that has at most N  leaves and can be used as a
proxy of T  for assembling hp-adaptive procedures. Under the standard assumptions about the
local errors, we prove that our approximation of complexity N  is bounded by (2N−1)σ n /(N-n+1),
where σ n , nN, is the best possible approximation of complexity n.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen