Galerkin Approximations for an Initial Boundary Problem of Transient Flow in Fractured Porous Media
Baigereyev D.R. Berdyshev A.S. Alimbekova N.B.
November 2022Pleiades Publishing
Lobachevskii Journal of Mathematics
2022#43Issue 113048 - 3056 pp.
Abstract: In this paper, theoretical estimates for the solution of an approximation problem for a fourth-order partial differential equation with fractional derivatives in the sense of Caputo are obtained. This equation describes a transient fluid flow in a fractured porous medium. To approximate fractional derivatives, a higher-order formula was applied, and a substep scheme technique was employed to retain a global higher-order convergence in the temporal variable. The method of a priori estimates is utilized to prove the unconditional stability of the proposed method with respect to the initial data and the right-hand side of the equation. The convergence of the approximate solution to the weak solution of the original differential problem is rigorously proved.
a priori estimate , convergence , fourth-order differential equation , fractional derivative in the sense of Caputo , stability
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Amanzholov University, Ust-Kamenogorsk, 070002, Kazakhstan
Abai Kazakh National Pedagogical University, Almaty, 050012, Kazakhstan
Amanzholov University
Abai Kazakh National Pedagogical University
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