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Towards adaptive finite element schemes for partial differential Volterra equation solvers

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Abstract

We give a brief indication of how elliptic, parabolic and hyperbolic partial differential equations with memory arise when modelling viscoelastic materials. We then point out the urgent need for adaptive solvers for these problems and, employing the methodology of Eriksson, Johnson et al. (e.g., SIAM J. Numer. Anal. 28 (1991)), we given ana posteriori error estimate for a model two-point hereditary boundary value problem. The strengths and weaknesses of the analysis and estimate are discussed.

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Authors and Affiliations

  1. BICOM, Brunel University, UB8 3PH, Uxbridge, UK

    Simon Shaw & J. R. Whiteman

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  1. Simon Shaw
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  2. J. R. Whiteman
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Dedicated to Professor J. Crank on the occasion of his 80th birthday

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Shaw, S., Whiteman, J.R. Towards adaptive finite element schemes for partial differential Volterra equation solvers. Adv Comput Math 6, 309–323 (1996). https://doi.org/10.1007/BF02127710

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