Natural hierarchical refinement for finite element methods
Krysl, Petr; Grinspun, Eitan; Schröder, Peter
International Journal for Numerical Methods in Engineering, Vol 56, Num 8, pp.1109 - 1124, February 2003
Department of Structural Engineering, University of California-San Diego, Mail code 0085, 9500 Gilman Drive, La Jolla, CA 92093-0085, U.S.A.
Peter Schröder and Eitan Grinspun
Department of Computer Science, California Institute of Technology, Mail code 256-80, Pasadena, CA 91125, U.S.A.
Abstract
Current formulations of adaptive finite element mesh refinement seem simple enough, but their implementations prove to be a formidable task. We offer an alternative point of departure which yields equivalent adapted approximation spaces wherever the traditional mesh refinement is applicable, but our method proves to be significantly simpler to implement. At the same time it is much more powerful in that it is general (no special tricks are required for different types of finite elements), and applicable for some newer approximations where traditional mesh refinement concepts are not of much help, for instance on subdivision surfaces.
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