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Dual error estimates for polygonal approximations of curved boundaries
Author(s) -
Wieners C.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<532::aid-pamm532>3.0.co;2-f
Subject(s) - corollary , dual (grammatical number) , approximations of π , mathematics , multigrid method , duality (order theory) , property (philosophy) , approximation error , numerical approximation , geometry , mathematical analysis , numerical analysis , partial differential equation , combinatorics , art , literature , philosophy , epistemology
In [3] we derived abstract criteria for the approximation property in multigrid analysis for non‐nested spaces (in the form given in [2]), and we discussed the application to domains with curved boundaries. As a corollary, we present here abstract criteria for duality estimates which finally leads to optimal dual estimates for polygonal approximations of solutions on nonpolygonal domains. The result is illustrated by a numerical experiment.