Geometrically Consistent Mesh Modification

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 mesh modification. We discuss the concept of discrete geometric consistency, show the failure of naive approaches, and propose and analyze a simple algorithm that is geometrically consistent and accuracy preserving. Key words. Mesh modification, manifold, parametric finite elements, accuracy preserving, geometric consistency, refinement, coarsening, smoothing, mean curvature, Willmore.

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: A. Bonito, R. H. Nochetto, M. S. Pauletti
• Keywords: Discrete Geometric Consistency, Geometric Consistency, Mesh Modification, SIAMNUM 2010