Notes on the finite element method and its generalization
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abstract
An effort was made to relate the weighting functions to the role of reducing the discretization errors, and relate the finite element method to a modified finite volume method. Furthermore, an effort was also made to formulate a generalization of the finite element method, and discuss the issues in weighting functions, residual, and realization of the integral form of the conservation laws in discretization. It is expected that this formulation will shed some light on the further development of the finite element method, and on the exploration of new discretization schemes in general.
