The pressure-robust virtual element methods with reconstruction for the Stokes equation
Abstract
Based on the idea of reconstruction, we develop a unified theoretical framework on the pressure-robust virtual element methods for Stokes equation. The reconstruction can be done on any shape-regular simplicial subdivision of polytopal elements and consists of two steps: the interpolation onto H(div)-conforming finite element space and the solution of a local problem element by element. By using this reconstruction we only modify the right-hand side of original virtual element methods in order to obtain the pressure-robust schemes with optimal convergence. This framework is applied to the conforming and nonconforming virtual element methods of arbitrary polynomial degree in two and three dimensions. In particular, we present the pressure-robust scheme for the nonconforming virtual element method and give some explanations on developing the pressure-robust conforming virtual element method by using this reconstruction. Numerical experiments confirm the optimal convergence rate for this nonconforming pressure-robust scheme and show that the velocity error is independent of the dynamic viscosity parameter as well as of large pressure gradients.
Related
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BibTeX
@misc{zhao2026pressurerobust,
title = {{The pressure-robust virtual element methods with reconstruction for the Stokes equation}},
author = {Jikun Zhao and Wenhao Zhu and Zhaonan Dong and Shipeng Mao},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://inria.hal.science/hal-05288123v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The pressure-robust virtual element methods with reconstruction for the Stokes equation
AU - Jikun Zhao
AU - Wenhao Zhu
AU - Zhaonan Dong
AU - Shipeng Mao
PY - 2026
DA - 2026/09/07
PB - HAL
UR - https://inria.hal.science/hal-05288123v2
AB - Based on the idea of reconstruction, we develop a unified theoretical framework on the pressure-robust virtual element methods for Stokes equation. The reconstruction can be done on any shape-regular simplicial subdivision of polytopal elements and consists of two steps: the interpolation onto H(div)-conforming finite element space and the solution of a local problem element by element. By using this reconstruction we only modify the right-hand side of original virtual element methods in order to obtain the pressure-robust schemes with optimal convergence. This framework is applied to the conforming and nonconforming virtual element methods of arbitrary polynomial degree in two and three dimensions. In particular, we present the pressure-robust scheme for the nonconforming virtual element method and give some explanations on developing the pressure-robust conforming virtual element method by using this reconstruction. Numerical experiments confirm the optimal convergence rate for this nonconforming pressure-robust scheme and show that the velocity error is independent of the dynamic viscosity parameter as well as of large pressure gradients.
ER -