2014
DOI: 10.1155/2014/642470
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Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient

Abstract: The paper presents a framework for the construction of Monte Carlo finite volume element method (MCFVEM) for the convection-diffusion equation with a random diffusion coefficient, which is described as a random field. We first approximate the continuous stochastic field by a finite number of random variables via the Karhunen-Loève expansion and transform the initial stochastic problem into a deterministic one with a parameter in high dimensions. Then we generate independent identically distributed approximatio… Show more

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“…Following the similar arguments in [30], we can obtain the estimates in Proposition 3.4. One can also refer to [31,32,42] for further details. Remark 3.2.…”
Section: Numerical Approximations Of Degenerate Fractional Conservati...mentioning
confidence: 99%
“…Following the similar arguments in [30], we can obtain the estimates in Proposition 3.4. One can also refer to [31,32,42] for further details. Remark 3.2.…”
Section: Numerical Approximations Of Degenerate Fractional Conservati...mentioning
confidence: 99%