Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 691-711.

We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain Ω 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.

Classification : 65N15, 35J60
Mots clés : nonlinear elliptic BVP, error estimates, nonstandard boundary condition, linearization
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     title = {Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Slodička, Marian. Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 691-711. http://archive.numdam.org/item/M2AN_2001__35_4_691_0/

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