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Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy. 相似文献
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If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a
Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative
entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here
that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states
the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov
chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may
even differ by a dimensional factor. 相似文献
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We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented. 相似文献
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