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Totally Discrete Explicit and Semi-implicit Euler Methods for a Blow-up Problem in Several Space Dimensions

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Abstract

The equation u t =Δu+u p with homogeneous Dirichlet boundary conditions has solutions with blow-up if p>1. An adaptive time-step procedure is given to reproduce the asymptotic behavior of the solutions in the numerical approximations. We prove that the numerical methods reproduce the blow-up cases, the blow-up rate and the blow-up time. We also localize the numerical blow-up set.

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  1. Instituto de Cálculo Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II Ciudad Universitaria (1428), Buenos Aires, Argentina

    Pablo Groisman

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Groisman, P. Totally Discrete Explicit and Semi-implicit Euler Methods for a Blow-up Problem in Several Space Dimensions. Computing 76, 325–352 (2006). https://doi.org/10.1007/s00607-005-0136-0

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