A Direct Discrete Formulation of Field Laws: The Cell Method

We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formu- lation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coin- cides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiff- ness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one obtained with FEM, using the same interpolation.

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