Classical ways to describe shape functions for finite element methods make use of interpolating or approximating schemes, for example, Taylor and Lagrange or Bézier. In this paper we outline the possibility of using iterative schemes first applied in the computation of fractal curves and surfaces. Our attempt will be restricted to shape functions defined over 2-simplices. Because of the fractal nature of the functions, we get only continuous or uniformly continuous functions. We see that they can be found as an attractor of a suitable iterated function system (IFS).
Fractal interpolation functions for a class of finite elements
DE MARCHI, Stefano;
1994-01-01
Abstract
Classical ways to describe shape functions for finite element methods make use of interpolating or approximating schemes, for example, Taylor and Lagrange or Bézier. In this paper we outline the possibility of using iterative schemes first applied in the computation of fractal curves and surfaces. Our attempt will be restricted to shape functions defined over 2-simplices. Because of the fractal nature of the functions, we get only continuous or uniformly continuous functions. We see that they can be found as an attractor of a suitable iterated function system (IFS).
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