Geodesic
Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 40-56
We consider the Stefan-type diffusion boundary-value problem with free boundary and nonlinear Neumann boundary conditions. Such problems describe hydride formation under constant conditions when nonlinear surface processes are taken into account. We construct the difference numerical method and prove the convergence of the interpolation approximations to the weak solution of the problem. Then we apply the theory of boundary-value problems to show that this weak solution is the classical solution. Thus, the existence of the solution to the problem is proved and the difference method is justified.
Classification : 65N06, 65N12, 35K20, 35K60, 35R35, 35A05
Keywords: Stefan-type problem, free boundary, nonlinear Neumann condition, existence of solution, difference scheme, uniform convergence of approximations 
@article{ETNA_2009__35__a13,
     author = {Chernov,  I.A.},
     title = {Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear {Neumann} boundary conditions},
     journal = {Electronic transactions on numerical analysis},
     pages = {40--56},
     year = {2009},
     volume = {35},
     zbl = {1171.65063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a13/}
}
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AU  - Chernov,  I.A.
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JO  - Electronic transactions on numerical analysis
PY  - 2009
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EP  - 56
VL  - 35
UR  - http://geodesic.mathdoc.fr/item/ETNA_2009__35__a13/
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ID  - ETNA_2009__35__a13
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%0 Journal Article
%A Chernov,  I.A.
%T Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions
%J Electronic transactions on numerical analysis
%D 2009
%P 40-56
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%U http://geodesic.mathdoc.fr/item/ETNA_2009__35__a13/
%G en
%F ETNA_2009__35__a13
Chernov,  I.A. Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions. Electronic transactions on numerical analysis, Tome 35 (2009), pp. 40-56. http://geodesic.mathdoc.fr/item/ETNA_2009__35__a13/