Short Note: A proof that a discrete delta function is second-order accurate

Authors:
J. Thomas Beale
Affiliations:
Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, United States
Venue:
Journal of Computational Physics
Year:
2008

Citing 11
Cited 4

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Abstract

It is proved that a discrete delta function introduced by Smereka [P. Smereka, The numerical approximation of a delta function with application to level set methods, J. Comput. Phys. 211 (2006) 77-90] 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 Mayo [A. Mayo, The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Numer. Anal. 21 (1984) 285-299]. It can be expressed naturally using a level set function.