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Fitted finite element discretization of two‐phase Stokes flow
Author(s) -
Agnese Marco,
Nürnberg Robert
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4237
Subject(s) - discretization , polygon mesh , finite element method , piecewise linear function , robustness (evolution) , smoothing , mathematics , piecewise , numerical analysis , stokes flow , flow (mathematics) , mathematical analysis , mathematical optimization , geometry , physics , biochemistry , chemistry , statistics , gene , thermodynamics
Summary We propose a novel fitted finite element method for two‐phase Stokes flow problems that uses piecewise linear finite elements to approximate the moving interface. The method can be shown to be unconditionally stable. Moreover, spherical stationary solutions are captured exactly by the numerical approximation. In addition, the meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations, a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments for our numerical method, which demonstrate the accuracy and robustness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.