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Insights on Global and Local Numbering Solutions in Element Node Calculations

This document explores the intricacies of local and global numbering systems in element node calculations. It details various methods for determining unknown and approximate solutions, providing insights into mathematical expressions and their applications. The discussion includes algorithms for solving equations involving elements, including their behavior under different conditions. Furthermore, the relationships between different variables and their implications on the overall solutions are analyzed, offering a comprehensive understanding of the subject.

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Insights on Global and Local Numbering Solutions in Element Node Calculations

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  1. Element Node Element numbers e 1 2 1 2 3 4 local 1 1 2 2 1 3 4 5 2 2 3 Global numbering global 3 3 4 4 4 5 Local numbering 1 2 +X

  2. u v ve(x) ve2 ve1 e +X 1 2 +X Unknown solution u(x) Approximate solution v(x) = Sve(x)

  3. ith element 1 2 x = 0 xi + X xi+1 x   = -1  = +1 hi

  4. v N N2 1 N1 ve2 ve1 0   2 2 1 1  = 0  = +1  = -1  = +1  = -1

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