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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Optimal $ L\sp{\infty }$ estimates for the finite element method on irregular meshes


Author: Ridgway Scott
Journal: Math. Comp. 30 (1976), 681-697
MSC: Primary 65N15
MathSciNet review: 0436617
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Abstract: Uniform estimates for the error in the finite element method are derived for a model problem on a general triangular mesh in two dimensions. These are optimal if the degree of the piecewise polynomials is greater than one. Similar estimates of the error are also derived in $ {L^p}$. As an intermediate step, an $ {L^1}$ estimate of the gradient of the error in the finite element approximation of the Green's function is proved that is optimal for all degrees.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0436617-2
PII: S 0025-5718(1976)0436617-2
Article copyright: © Copyright 1976 American Mathematical Society