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Error estimates for multidimensional singular parabolic problems

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Abstract

We consider a rather general class of singular parabolic problems; multidimensional two-phase Stefan problem and porous-medium equation involving additional nonlinearities are included. We analyze an approximation scheme consisting in a regularization procedure and discretization by means ofC °-piecewise linear finite elements in space and backward-differences in time. We prove severalL β-error estimates for the various unknowns, wherep depends on the problem. As a by-product of our technique, we obtain an optimalL 2-error estimate for enthalpy.

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Authors and Affiliations

  1. Instituto de Desarrollo Technológico para la Industria Química, Programa Especial de Matemática Aplicada, 3000, Santa Fe, Argentina

    Ricardo H. Nochetto

  2. Istituto di Analisi Numerica del C.N.R., 27100, Pavia, Italy

    Ricardo H. Nochetto

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  1. Ricardo H. Nochetto
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This work was supported by “Consejo Nacional de Investigaciones Cientificas y Técnicas” of Argentina.

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Nochetto, R.H. Error estimates for multidimensional singular parabolic problems. Japan J. Appl. Math. 4, 111–138 (1987). https://doi.org/10.1007/BF03167758

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