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Adaptive Approximation
Author(s) -
Lippold G.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670915
Subject(s) - monotone polygon , mathematics , sequence (biology) , finite element method , set (abstract data type) , adaptive mesh refinement , partial differential equation , mathematical optimization , mathematical analysis , computer science , geometry , physics , thermodynamics , genetics , computational science , biology , programming language
The adaptivity of transitions on the mesh sequence ℋ in some mesh refinement structure is defined as a selection strategy which is performed by means of a monotone local indicator on the set of cells in that structure. Adaptivity then turns out to be a local optimality property relative to some maximum or sum indicator on ℋ. – Adaptive transitions generate optimal mesh sequences. The notion of δ‐adaptivity is introduced to catch problems where only perturbed error indicators are available. δ‐adaptive transitions generate quasi‐optimal mesh sequences. – For the solution of one‐dimensional elliptic boundary value problems by linear finite elements δ‐adaptive transitions are defined by means of the local defects in the differential equation which are caused by the finite element solutions.