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

Slodička, Marian

Slodička, Marian

ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 691-711

Résumé

We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain $Ω \subset ℝ^{dim}$ 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 $L_{\infty} (Ω)$ spaces.

MR Zbl

Classification : 65N15, 35J60
Keywords: nonlinear elliptic BVP, error estimates, nonstandard boundary condition, linearization

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     author = {Slodi\v{c}ka, Marian},
     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},
     pages = {691--711},
     year = {2001},
     publisher = {EDP Sciences},
     volume = {35},
     number = {4},
     mrnumber = {1862875},
     zbl = {0997.65124},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_2001__35_4_691_0/}
}

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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. https://www.numdam.org/item/M2AN_2001__35_4_691_0/

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