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Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions

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Abstract

We formulate and analyze a Crank-Nicolson finite element Galerkin method and an algebraically-linear extrapolated Crank-Nicolson method for the numerical solution of a semilinear parabolic problem with nonlocal boundary conditions. For each method, optimal error estimates are derived in the maximum norm.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, Colorado School of Mines, 80401-1887, Golden, CO, USA

    G. Fairweather

  2. Departamento de Matemática Aplicada y Computación, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain

    J. C. López-Marcos

Authors
  1. G. Fairweather
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  2. J. C. López-Marcos
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Additional information

Dedicated to Professor J. Crank on the occasion of his 80th birthday

Supported in part by the National Science Foundation grant CCR-9403461.

Supported in part by project DGICYT PB95-0711.

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Fairweather, G., López-Marcos, J.C. Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Adv Comput Math 6, 243–262 (1996). https://doi.org/10.1007/BF02127706

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