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

Marian Slodička

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

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

Abstract

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We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain Ω ⊂ 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 Γ 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 ( Ω ) , H 1 ( Ω ) and L ∞ ( Ω ) spaces.

How to cite

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Slodička, 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 -

References

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