Consistency, Stability, a-Priori and a-Posteriori Errors for Nonlinear Problems

In an abstract framework similar to the one developed in Crouzeix-Rappaz [2], we present a formalism which makes precise the notions of consistency and stability for the finite element approximation of nonlinear elliptic problems. The consistency is connected to the approximation by interpolation, whereas the stability follows from discrete inf-sup conditions of the linearized problem. Moreover, contrary to the method developed in [2], this formalism does not require us to invert the principal part of the operator and allows us to obtain a priori and a posteriori error estimates for strongly nonlinear problems.


Published in:
Comptes Rendus De L Academie Des Sciences Serie I-Mathematique, 312, 9, 699-703
Year:
1991
ISSN:
0764-4442
Keywords:
Note:
Pousin, j, ecole polytech fed lausanne,dept math,ch-1015 lausanne,switzerland.
ISI Document Delivery No.: FJ488
Times Cited: 4
Cited Reference Count: 5
Laboratories:




 Record created 2006-08-24, last modified 2018-12-03


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