Abstract
AbstractThis paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher‐dimensional spaces, independent of specific co‐ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non‐Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
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