Publications [#243361] of J. Thomas Beale
- Beale, JT, A proof that a discrete delta function is second-order accurate,
Journal of Computational Physics, vol. 227 no. 4
pp. 2195-2197, Elsevier BV, ISSN 0021-9991 [pdf], [doi]
(last updated on 2019/04/20)
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. © 2007 Elsevier Inc. All rights reserved.