scholarly journals The finite element method with Lagrange multipliers for domains with corners

1981 ◽  
Vol 37 (155) ◽  
pp. 13-13 ◽  
Author(s):  
Juhani Pitk{äranta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lagrange Multipliers ◽  
The Finite Element Method ◽  
Domains With Corners ◽  
Element Method

On Certain Approximations in the Finite-Element Method

1971 ◽  
Vol 38 (1) ◽  
pp. 58-61 ◽  
Author(s):  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Variational Principle ◽  
Lagrange Multipliers ◽  
Restricted Problem ◽  
Generalized Variational Principle ◽  
The Finite Element Method ◽  
Element Method

Approximations made outside of the variational principle used in the finite-element method are examined for a restricted problem in elasticity. They are shown to be rigorous from the standpoint of a generalized variational principle in which Lagrange multipliers are utilized. The convergence of the Ritz solution to the exact solution is demonstrated. The bound is shown to be a function of the quality of both the displacement functions and other approximate functions in the analysis.

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