Analysis of optimal finite-element meshes in

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