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math.NA2024
A virtual element method with IMEX-SAV scheme for the incompressible magnetohydrodynamics equations
Xiaojing Dong, Yunqing Huang, Tianwen Wang
This paper proposes a virtual element method (VEM) combined with a second-order implicit-explicit scheme based on the scalar auxiliary variable (SAV) method for the incompressible…
math.NA2024
Conservative nonconforming virtual element method for stationary incompressible magnetohydrodynamics
Xiaojing Dong, Yunqing Huang, Tianwen Wang
In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element sat…
math.NA2024
The grad-div conforming virtual element method for the quad-div problem in three dimensions
Xiaojing Dong, Yibing Han, Yunqing Huang
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsy…