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A convergence rate theorem for finite difference approximations to delta functions. (English) Zbl 1155.65016
A new rate of convergence for approximations to certain integrals over codimension one manifolds in $$\mathbb R^n$$, is proved. The type of manifold is defined by the zero level set of a smooth mapping $$u:\mathbb R^n\to\mathbb R$$. The approximation method used, is based on two finite difference methods for the discretizing of the delta function, originally presented by the author in a previous research work [J. Comput. Phys. 220, No. 2, 915–931 (2007; Zbl 1115.65028)], were empirical convergence rates had indicated the first and second order accuracy. In this work these convergence rates are proved for the two proposed algorithms, under fairly general hypotheses.

##### MSC:
 65D15 Algorithms for approximation of functions
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##### References:
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