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Mathematics of Computation

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Optimal $L^{\infty }$ 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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Article copyright: © Copyright 1976 American Mathematical Society