21 research outputs found

    Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

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    In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

    Non-Fickian tracer transport in porous media

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    Diffusion processes have traditionally been modeled using the classical diffusion equation. However, as in the case of tracer transport in porous media, significant discrepancies between experimental results and numerical simulations have been reported in the literature. Therefore, in order to describe such anomalous behavior known as non-Fickian diffusion, some authors have replaced the parabolic model by continuous random walk models, which have been shown to be very effective. Integro-differential models have been also proposed to describe non-Fickian diffusion in porous media. The aim of this paper is to compare the ability of these classes of models to capture the dynamics of tracer transport in porous media
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