Numerical approximation of a parabolic problem with a nonlinear boundary condition
R.G. Duran - Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina (email)
We analyze numerical approximations of positive solutions of a
heat equation with a nonlinear flux condition which produces
blow up of the solutions. By a semidiscretization using
finite elements in the space variable we obtain a system
of ordinary differential equations which is expected to be an approximation
of the original problem. Our objective is to analyze whether
this system has a similar behaviour than the original
problem. We find a necessary and sufficient condition for
blow up of this system. However, this condition is slightly
different than the one known for the original problem, in particular,
there are cases in which the continuous problem has blow up while
its semidiscrete approximation does not.
Keywords: Nonlinear boundary conditions, blow up, numerical approximations.
Received: July 1996; Revised: August 1997; Published: April 1998.
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