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A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces

Derrick Jones, Xu Zhang
2021 Electronic Research Archive  

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In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements for one velocity component and non-conforming linear elements for the other velocity component. The pressure is approximated by piecewise constant. Unisolvency, among other fundamental properties of the new vector-valued IFE functions, is analyzed. Based on the new IFE spaces,
more » ... te and full-discrete schemes are developed for solving the unsteady Stokes equations with a stationary or a moving interface. Re-meshing is not required in our numerical scheme for solving the moving-interface problem. Numerical experiments are carried out to demonstrate the performance of this new IFE method. 2020 Mathematics Subject Classification. Primary: 65N15, 65N30; Secondary: 35R05.
doi:10.3934/era.2021032 fatcat:vyr2svrjazdbtacgfftd44hyri
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Derrick Jones, Xu Zhang. "A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces." Electronic Research Archive 29.5 (2021)