NUMERICAL RESEARCH OF THE BARENBLATT--ZHELTOV--KOCHINA MODEL ON THE INTERVAL WITH WENTZELL BOUNDARY CONDITIONS

Abstract

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 $L^2(0,1)$.