Lecture Notes: Introduction to Finite Element Method |
Chapter 4. FE Modeling and Solution Techniques |
V. Numerical Error
Error ≠Mistakes in FEM (modeling or solution).
Type of Errors:
•Modeling Error (beam, plate … theories)
•Discretization Error (finite, piecewise …)
•Numerical Error ( in solving FE equations)
Example (numerical error):
u1 u2 P 
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1 k1 2 k2 |
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FE Equations:
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−k1 u1 |
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−k1 |
k1 + k2 u2 |
0 |
and Det K = k1k2 .
The system will be singular if k2 is small compared with k1.
© 1997-2002 Yijun Liu, University of Cincinnati |
114 |
Lecture Notes: Introduction to Finite Element Method |
Chapter 4. FE Modeling and Solution Techniques |
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k2 << k1 (two lines close): Ö System ill-conditioned.
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u2 = k1 k+1 k2 u1
k2 >> k1 (two line apart):
Ö System well conditioned.
P/k1 u1
•Large difference in stiffness of different parts in FE model may cause ill-conditioning in FE equations. Hence giving results with large errors.
•Ill-conditioned system of equations can lead to large changes in solution with small changes in input (right hand side vector).
© 1997-2002 Yijun Liu, University of Cincinnati |
115 |