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

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.