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Mathematics of Computation

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Finite element interpolation of nonsmooth functions satisfying boundary conditions

Authors: L. Ridgway Scott and Shangyou Zhang
Journal: Math. Comp. 54 (1990), 483-493
MSC: Primary 65D05; Secondary 65N30
MathSciNet review: 1011446
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Abstract: In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on d- or $(d - 1)$-simplices to generate nodal values for the interpolation operator. This combination of averaging and interpolation is shown to be a projection, and optimal error estimates are proved for the projection error.

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Article copyright: © Copyright 1990 American Mathematical Society