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Optimal Iterative Refinement Methods
Excerpt from Optimal Iterative Refinement Methods
We assume that all the elements are shape regular in the sense that there is a uniform bound on hk/pk. Here hk and pk are the diameter and the radius of the largest inscribed sphere of any element K, respectively. Our bounds in the theory developed below also depend on the shape of the subregions Q,. Thus in order for our proofs to work, we cannot allow the sets qi to become arbitrarily thin in comparison with the diameter of Q,_1. We also assume that the area of any triangle on level i can be bounded by const. Qj'i, j i times the area of the triangle on level j of which it is a part. Here q is a constant 1.
We assume that all the elements are shape regular in the sense that there is a uniform bound on hk/pk. Here hk and pk are the diameter and the radius of the largest inscribed sphere of any element K, respectively. Our bounds in the theory developed below also depend on the shape of the subregions Q,. Thus in order for our proofs to work, we cannot allow the sets qi to become arbitrarily thin in comparison with the diameter of Q,_1. We also assume that the area of any triangle on level i can be bounded by const. Qj'i, j i times the area of the triangle on level j of which it is a part. Here q is a constant 1.
24 pages, Paperback
Published August 24, 2018
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