On a parabolic problem with nonlinear Newton boundary conditions. (English) Zbl 1090.35102

The paper is concerned with a parabolic convection-diffusion initial-boundary value problem equipped with mixed Dirichlet-nonlinear Newton boundary condition in a two-dimensional domain. Existence and uniqueness of a week solution to the continuous problem is proved for the case of Lipschitz-continuous Newton boundary condition and the finite element approximation is analyzed. The convergence of the finite element method is proved. The paper is a generalization of analytical as well as numerical results for the elliptic case to the parabolic problem. There are numerous practical applications of this approach.


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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