@article {DOKKEN2020113129,
	title = {A multimesh finite element method for the Navier{\textendash}Stokes equations based on projection methods},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	volume = {368},
	year = {2020},
	pages = {113129},
	publisher = {Elsevier},
	abstract = {The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche{\textquoteright}s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier{\textendash}Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor{\textendash}Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek{\textendash}Sch{\"a}fer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel.},
	keywords = {Incremental pressure-correction scheme, Multimesh finite element method, Navier{\textendash}Stokes equations, Nitsche{\textquoteright}s method, Projection method},
	issn = {0045-7825},
	doi = {https://doi.org/10.1016/j.cma.2020.113129},
	url = {http://www.sciencedirect.com/science/article/pii/S0045782520303145},
	author = {J{\o}rgen Schartum {Dokken} and Johansson, August and Massing, Andre and Simon W {Funke}}
}
