DOI: 10.1002/mma.70992 ISSN: 0170-4214

Method of Fictitious Domain for the System of Kelvin–Voigt Equations

Zhanybek Baitulenov, Serik Aitzhanov, Yermek Alimzhanov
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ABSTRACT

In this paper a type of the fictitious domain method with continuation over lower‐order coefficients for a homogeneous, nonlinear, non‐stationary Kelvin–Voigt model in a three‐dimensional domain is investigated. The existence, uniqueness, and convergence of a generalized solution to the auxiliary problem are proven globally in time. Locally in time, the existence and convergence of a unique strong solution are established, and for the strong solution, a higher‐order convergence rate estimate is derived compared to the “classical” version of the fictitious domain method.

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