DEPARTAMENTO DE MATEMÁTICA DOCUMENTO DE TRABAJO “ Adaptive Numerical Schemes for a Parabolic Problem with Blow – Up ”

@inproceedings{Ferreira2002DEPARTAMENTODM,
  title={DEPARTAMENTO DE MATEM{\'A}TICA DOCUMENTO DE TRABAJO “ Adaptive Numerical Schemes for a Parabolic Problem with Blow – Up ”},
  author={Raul S. Ferreira and Pablo Groisman and Julio D. Rossi},
  year={2002}
}
In this paper we present adaptive procedures for the numerical study of positive solutions of the following problem,    ut = uxx (x, t) ∈ (0, 1)× [0, T ), ux(0, t) = 0 t ∈ [0, T ), ux(1, t) = u(1, t) t ∈ [0, T ), u(x, 0) = u0(x) x ∈ (0, 1), with p > 1. We describe two methods, the first one refines the mesh in the region where the solution becomes bigger in a precise way that allows us to recover the blow-up rate and the blow-up set of the continuous problem. The second one combine the… CONTINUE READING

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