Neuro-fuzzy finite element method and a posteriori error estimation

In this paper, we propose a neuro-fuzzy finite element method with an iterative learning scheme, as an application of Gaussian radial basis function (RBF) networks, in which the finite elements are fuzzy subsets defined by Gaussian membership functions. For almost all problems in practical engineering where FEM is applied, analytical solutions are not obtained. Since the finite element concept is based on the discretization of a continuum, the subject of developing reliable a posteriori error estimates is central to the effective use of FEM. In the FEM some error estimators which are reasonably accurate and useful in the existing problem have been proposed. The approximate solutions of neuro-fuzzy FEM also need some tools for error estimation. Hence, we propose a method of error estimation based on the same iterative learning scheme. Illustrative examples of solving Laplace equations are shown with the computational results of approximate solutions and estimated errors by using the proposed methods