Geometrically Consistent Mesh Modification

Authors:
A. Bonito;R. H. Nochetto;M. S. Pauletti
Affiliations:
bonito@math.tamu.edu and pauletti@math.tamu.edu;rhn@math.umd.edu;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving.