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Analysis of optimal finite-element meshes in $ {\bf R}\sp{1}$


Authors: I. Babuška and W. C. Rheinboldt
Journal: Math. Comp. 33 (1979), 435-463
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1979-0521270-2
MathSciNet review: 521270
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Abstract: A theory of a posteriori estimates for the finite-element method was developed earlier by the authors. Based on this theory, for a two-point boundary value problem the existence of a unique optimal mesh distribution is proved and its properties analyzed. This mesh is characterized in terms of certain, easily computable local error indicators which in turn allow for a simple adaptive construction of the mesh and also permit the computation of a very effective a posteriori error bound. While the error estimates are asymptotic in nature, numerical experiments show the results to be excellent already for 10


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DOI: https://doi.org/10.1090/S0025-5718-1979-0521270-2
Article copyright: © Copyright 1979 American Mathematical Society

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