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Delta function approximations in level set methods by distance function extension. (English) Zbl 1186.65018
Summary: A.-K. Tornberg and B. Engquist [ibid. 200, No. 2, 462–488 (2004; Zbl 1115.76392)], it was shown for simple examples that the most common way to regularize delta functions in connection to level set methods produces inconsistent approximations with errors that are not reduced with grid refinement. Since then, several clever approximations have been derived to overcome this problem. However, the great appeal of the old method was its simplicity.
In this paper it is shown that the old method – a one-dimensional delta function approximation extended to higher dimensions by a distance function – can be made accurate with a different class of one-dimensional delta function approximations. The prize to pay is a wider support of the resulting delta function approximations.

65D15 Algorithms for approximation of functions
Full Text: DOI
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