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A proof that a discrete delta function is second-order accurate. (English) Zbl 1136.65017
Summary: It is proved that a discrete delta function introduced by P. Smereka, ibid. 211, No. 1, 77–90 (2006; Zbl 1086.65503)] gives a second-order accurate quadrature rule for surface integrals using values on a regular background grid. The delta function is found using a technique of A. Mayo [SIAM J. Numer. Anal. 21, No. 2, 285–299 (1984; Zbl 1131.65303)]. It can be expressed naturally using a level set function.

MSC:
65D15 Algorithms for approximation of functions
46F10 Operations with distributions and generalized functions
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