On Asymptotically Optimal Meshes by Coordinate Transformation

Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.289-306, September 17-20 2006

MESHING
RESEARCH
CORNER

15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 17-20, 2006

Harvard University
{gdiez|sjg}@cs.harvard.edu

Abstract
We study the problem of constructing asymptotically optimal meshes with respect to the gradient error of a given input function. We provide simpler proofs of previously known results and show constructively that a closed-form solution exists for them. We show how the transformational method for obtaining meshes, as is, cannot produce asymptotically optimal meshes for general inputs. We also discuss possible variations of the problem definition that may allow for some forms of optimality to be proved.

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