Variational crimes and error estimates in the finite element method
Author:
Charles I. Goldstein
Journal:
Math. Comp. 35 (1980), 11311157
MSC:
Primary 65N30; Secondary 65N15
MathSciNet review:
583491
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Abstract: In order to numerically solve a secondorder linear elliptic boundary value problem in a bounded domain, using the finite element method, it is often necessary in practice to violate certain assumptions of the standard variational formulation. Two of these "variational crimes" will be emphasized here and it will be shown that optimal error estimates still hold. The first "crime" occurs when a nonconforming finite element method is employed, so that smoothness requirements are violated at interelement boundaries. The second "crime" occurs when numerical integration is employed, so that the bilinear form is perturbed. In both cases, the "patch test" is crucial to the proof of estimates, just as it was in the case of meansquare estimates.
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DOI:
http://dx.doi.org/10.1090/S00255718198005834910
PII:
S 00255718(1980)05834910
Article copyright:
© Copyright 1980
American Mathematical Society
