Locking and Robustness in The Finite
نویسنده
چکیده
In this paper we discuss locking and robustness of the nite element method for a model circular arch problem. It is shown that in the primal variable (i.e., the standard displacement formulation), the p-version is free from locking and uniformly robust with order p ?k and hence exhibits optimal rate of convergence. On the other hand, the h-version shows locking of order h ?2 , and is uniformly robust with order h p?2 for p > 2 which explains the fact that the quadratic element for some circular arch problems suuers from locking for thin arches in computational experience. If mixed method is used, both the h-version and the p-version are free from locking. Furthermore, the mixed method even converges uniformly with an optimal rate for the stress.
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