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Gradient-finite element method for nonlinear Neumann problems

Faragó I., Karátson J.

Journal of Applied Analysis

2001

Vol. 7, nr 2

257-269

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.