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- W2105000651 abstract "Abstract The finite element method is nowadays the most general and one of the most powerful tools for the analysis of structures. It is also a general mathematical technique and the main concern of the paper is to present it in this light. Functional Analysis is used as the ideal frame for a general abstract formulation. The ability to predict convergence to the exact solution of a sequence of approximate solutions obtained from patterns of finite elements with decreasing size is fundamental in the application of the method. In case conformity between elements is obtained, the finite element method is a particular case of Ritz's method, so that convergence can be ensured as far as completeness is achieved. A general completeness criterion is justified in the paper. Such criterion requires that the field components and all their derivatives, of order not higher than the highest order of derivative entering into the energy density expression, can take up any constant value within the element. It is finally proved that such criterion is also a general convergence criterion, i.e. a sufficient condition for convergence even if conformity is not achieved." @default.
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- W2105000651 date "1968-10-01" @default.
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- W2105000651 title "Theoretical foundations of the finite element method" @default.
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- W2105000651 doi "https://doi.org/10.1016/0020-7683(68)90014-0" @default.
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