Using Finite Elements Method on a PDE With No Solution 1.0

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
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