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Numerical analysis of approximation error for a nonlinear parabolic problem with terms concentrating in an oscillatory neighborhood of the boundary |
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PP: 455-462 |
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doi:10.18576/amis/180219
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Author(s) |
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Daniel Morales,
Gleiciane da Silva Araga ̃o,
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Abstract |
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| Numerically, we verify the theoretical results about the behavior of the solutions of a nonlinear parabolic problem with homogeneous Neumann boundary conditions, when a nonlinear reaction term is concentrated in a neighborhood of the boundary of a domain in R2, using the finite element method. We assume that this neighborhood shrinks to the boundary as a parameter ε goes to zero. Also, we suppose that the “inner boundary” of this neighborhood presents an oscillatory behavior. We evaluate the error made when the numerical solution of a parabolic problem with nonlinear Neumann boundary conditions is approximated by the family of numerical solutions of the concentrated problem, as ε goes to zero. Numerical results associated with the dynamics of these concentrated problems will be presented as a great novelty.
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