A POSTERIORI ERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS

1999 ◽  
Vol 09 (02) ◽  
pp. 261-286 ◽  
Author(s):  
SLIMANE ADJERID ◽  
JOSEPH E. FLAHERTY ◽  
IVO BABUŠKA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Method Of Lines ◽  
Posteriori Error ◽  
Parabolic Problems ◽  
A Posteriori ◽  
Element Discretization ◽  
Mesh Spacing ◽  
A Posteriori Estimates ◽  
Element Method

Babuška and Yu constructed a posteriori estimates for finite element discretization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edges as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabolic partial differential equations on square-element meshes. Error estimates computed in this manner are proven to be asymptotically correct; thus, they converge in strain energy under mesh refinement at the same rate as the actual errors.

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