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Using Finite Elements Method on a PDE With No Solution 1.0

  Date Added: August 07, 2013  |  Visits: 215

Using Finite Elements Method on a PDE With No Solution

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A simple partial differential equation (PDE) with boundary conditions is examined:d/dx( x dy/dx ) = xy(0) = y(1) = 0.Integrate the PDE twice to get its solution. Then apply the boundary conditions and get a contradiction. The boundary value problem(BVP)has no solution.Regardless, apply the finite elements method (FEM) using piecewise linear basis functions. The FEM is successfully completed without a hitch. There is no sign that the problem is insolvable.This occurs because the FEM makes assumptions which restrict the solution space. Within this restricted space the BVP does have a solution.The point is that one cannot blindly rely on a numerical technique to produce the correct answer to a problem. Numerical methods need to be supplemented with analysis.

Requirements: No special requirements
Platforms: Matlab
Keyword: Assumptions Insolvable Makes Problem Restrict Space
Users rating: 0/10

License: Shareware Size: 163.84 KB
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