Consistency, Stability, a-Priori and a-Posteriori Errors for Petrov-Galerkin Methods Applied to Nonlinear Problems

In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situations, strongly nonlinear elliptic problems. This formalism gives rise to a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods applied to elliptic nonlinear problems. This theory is illustrated with the example: -div (k(u)DELTAu) + c. DELTAu = f in a two dimensional domain OMEGA with Dirichlet boundary conditions.


Published in:
Numerische Mathematik, 69, 2, 213-231
Year:
1994
ISSN:
0029-599X
Note:
Cited Reference Count: 15
Laboratories:




 Record created 2006-08-24, last modified 2018-03-17


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