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Lagrange Interpolation Polynomials 1-Finite Element Method-Assignment Solution, Exercises of Mathematical Methods for Numerical Analysis and Optimization

Aligarh Muslim UniversityMathematical Methods for Numerical Analysis and Optimization

This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Nodes, Quadratic, One-dimensional, Element, Shape, Functions, Polynomials, Lagrange, interpolation

Typology: Exercises

2011/2012

Uploaded on 07/08/2012

ramu
ramu 🇮🇳

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Problem 4.18
The nodes of a quadratic one-dimensional element are located at x=0, x=l/2, and x=l. Express the shape
functions using Lagrange interpolation polynomials.
Solution
Ø(x) can be expressed in terms of three-station Lagrange interpolation polynomial as:
where
Substituting x1 = 0, x2 = l/2, x3 = l ; we get the required shape
functions as:
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Download Lagrange Interpolation Polynomials 1-Finite Element Method-Assignment Solution and more Exercises Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity!

Problem 4.

The nodes of a quadratic one-dimensional element are located at x=0, x=l/2, and x=l. Express the shape functions using Lagrange interpolation polynomials.

Solution

Ø(x) can be expressed in terms of three-station Lagrange interpolation polynomial as:

where

Substituting x 1 = 0, x 2 = l/2, x 3 = l ; we get the required shape

functions as:

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