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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 35.4 (2010): 691-711. <http://eudml.org/doc/197607>.

@article{Slodička2010,

abstract = {
We consider a nonlinear second order elliptic boundary
value problem (BVP)
in a bounded domain $\Omega\subset \{\mathbb R\}^N$ 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 Γn.
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
L2(Ω),H1(Ω) and L∞(Ω) spaces.
},

author = {Slodička, Marian},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

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

language = {eng},

month = {3},

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/197607},

volume = {35},

year = {2010},

}

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

DA - 2010/3//

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 $\Omega\subset {\mathbb R}^N$ 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 Γn.
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
L2(Ω),H1(Ω) and L∞(Ω) spaces.

LA - eng

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

UR - http://eudml.org/doc/197607

ER -

## References

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