### Abstract

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.

Original language | English |
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Pages (from-to) | 257-269 |

Number of pages | 13 |

Journal | Journal of Applied Analysis |

Volume | 7 |

Issue number | 2 |

Publication status | Published - Dec 2001 |

### Fingerprint

### Keywords

- Factorization
- Gradient-finite element method
- Neumann boundary value problems
- Non-injective nonlinear operator

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematical Physics
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics

### Cite this

**Gradient-finite element method for nonlinear neumann problems.** / Faragó, I.; Karátson, J.

Research output: Contribution to journal › Article

*Journal of Applied Analysis*, vol. 7, no. 2, pp. 257-269.

}

TY - JOUR

T1 - Gradient-finite element method for nonlinear neumann problems

AU - Faragó, I.

AU - Karátson, J.

PY - 2001/12

Y1 - 2001/12

N2 - 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.

AB - 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.

KW - Factorization

KW - Gradient-finite element method

KW - Neumann boundary value problems

KW - Non-injective nonlinear operator

UR - http://www.scopus.com/inward/record.url?scp=84867959911&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867959911&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 257

EP - 269

JO - Journal of Applied Analysis

JF - Journal of Applied Analysis

SN - 1425-6908

IS - 2

ER -