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The numerical approximation of a delta function with application to level set methods. (English) Zbl 1086.65503
Summary: It is shown that a discrete delta function can be constructed using a technique developed by A. Mayo [SIAM J. Numer. Anal. 21, No. 2, 285–299 (1984)] for the numerical solution of elliptic equations with discontinuous source terms. This delta function is concentrated on the zero level set of a continuous function. In two space dimensions, this corresponds to a line and a surface in three space dimensions. Delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function. The numerical implementation of these delta functions achieves the expected order of accuracy.
Reviewer: Reviewer (Berlin)

MSC:
65D15 Algorithms for approximation of functions
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N06 Finite difference methods for boundary value problems involving PDEs
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