The Complex Variable Boundary Element Method or CVBEM has recently been applied to the use of new fractal basis functions for defining a global trial function on the problem domain. In that recent advance, a topic for future research was the need for development of an algorithm to construct a global trial function that converges to the true problem boundary conditions, assumed to be continuous on the boundary. In this paper, such an algorithm for constructing a sequence of fractal basis functions is presented.
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