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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...
We present here a discretization of
a nonlinear oblique
derivative boundary value problem for the heat equation in dimension
two.
This finite difference scheme takes advantages of the
structure of the boundary condition, which can be reinterpreted as a
Burgers equation in the space variables. This enables to obtain an
energy estimate and to prove the convergence of the scheme.
We also provide some numerical simulations of this
problem and a numerical study of the stability of the scheme, which
appears...
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