# Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition

- Volume: 35, Issue: 4, page 691-711
- ISSN: 0764-583X

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topSlodička, Marian. "Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 691-711. <http://eudml.org/doc/194069>.

@article{Slodička2001,

abstract = {We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain $\Omega \subset \{\mathbb \{R\}\}^\dim $ with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part $\Gamma _n$. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization algorithm are derived in $L_\{2\} (\Omega ),H^\{1\}(\Omega )$ and $L_\{\infty \} (\Omega )$ spaces.},

author = {Slodička, Marian},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {nonlinear elliptic BVP; error estimates; nonstandard boundary condition; linearization; nonlinear elliptic boundar value problem; nonstandard boundary conditions; convergence; numerical examples},

language = {eng},

number = {4},

pages = {691-711},

publisher = {EDP-Sciences},

title = {Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition},

url = {http://eudml.org/doc/194069},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Slodička, Marian

TI - Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 4

SP - 691

EP - 711

AB - We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain $\Omega \subset {\mathbb {R}}^\dim $ with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part $\Gamma _n$. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization algorithm are derived in $L_{2} (\Omega ),H^{1}(\Omega )$ and $L_{\infty } (\Omega )$ spaces.

LA - eng

KW - nonlinear elliptic BVP; error estimates; nonstandard boundary condition; linearization; nonlinear elliptic boundar value problem; nonstandard boundary conditions; convergence; numerical examples

UR - http://eudml.org/doc/194069

ER -

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