Introduction To Finite Element Analysis And Design
Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
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Chapter 2, Problem 9E

Solve the differential equation in problem 8 for the following boundary conditions using the Galerkin method: u ( 0 ) = 1 , u ( 1 ) = 2 .

Assume the approximate solution as: u ˜ ( x ) = ϕ 0 ( x ) + c 1 ϕ ( x ) , where ϕ 0 ( x ) is a function that satisfies the essential boundary conditions, and ϕ 2 ( x ) is the weight function that satisfies the homogeneous part of the essential boundary conditions, that is. ϕ 1 ( 0 ) = ϕ 1 ( 1 ) = 0 . Hence, assume the functions as follows: ϕ 0 ( x ) = 1 + x , ϕ 1 ( x ) = x ( 1 x ) .

Compare the approximate solution with the exact solution by plotting their graphs. The exact solution can be derived as: u ( x ) = 2.9231 sin x + cos x x .

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