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.
WOS:A1991FJ48800009
1991
312
9
699
703
Pousin, j, ecole polytech fed lausanne,dept math,ch-1015 lausanne,switzerland.
ISI Document Delivery No.: FJ488
Cited Reference Count: 5
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