Geodesic
Numerical research of the Barenblatt -- Zheltov -- Kochina model on the interval with Wentzell boundary conditions
Journal of computational and engineering mathematics, Tome 6 (2019) no. 3, pp. 14-25

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In terms of numerical research, we study the Barenblatt – Zheltov – Kochina model, which describes dynamics of pressure of a filtered fluid in a fractured-porous medium with the general Wentzell boundary conditions. Based on the theoretical results associated with Galerkin method, we develop an algorithm and implement the numerical solution of the Cauchy-Wentzell problem on the interval $[0, 1]$. In particular, we examine the asymptotic approximation of the spectrum of the one-dimensional Laplace operator and present result of a computational experiment. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space $L^2(0, 1)$.
Keywords: Barenblatt – Zheltov – Kochina equation, Wentzell boundary conditions, numerical research, Galerkin method. 
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     author = {N. S. Goncharov},
     title = {Numerical research of the {Barenblatt} -- {Zheltov} -- {Kochina} model on the interval with {Wentzell} boundary conditions},
     journal = {Journal of computational and engineering mathematics},
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N. S. Goncharov. Numerical research of the Barenblatt -- Zheltov -- Kochina model on the interval with Wentzell boundary conditions. Journal of computational and engineering mathematics, Tome 6 (2019) no. 3, pp. 14-25. http://geodesic.mathdoc.fr/item/JCEM_2019_6_3_a1/