Geodesic
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 691-711

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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.

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: Mathematical Modelling and Numerical Analysis },
     pages = {691--711},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1862875},
     zbl = {0997.65124},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 691-711. http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_691_0/