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A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.

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Title: A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.
Authors: Xiong, Yu1 (AUTHOR) xtuyuriyxiong@gmail.com, Chen, Yanping2 (AUTHOR) ypchen@njupt.edu.cn, Zhou, Jianwei3 (AUTHOR) jwzhou@yahoo.com, Zhou, Yanping4 (AUTHOR) zhyp5208@163.com, Huang, Jian1 (AUTHOR) huangjian213@xtu.edu.cn
Source: Journal of Scientific Computing. Feb2026, Vol. 106 Issue 2, p1-35. 35p.
Abstract: This article investigates both a priori and a posteriori error estimates for a pressure-robust and divergence-free virtual element method to approximate the incompressible Brinkman problem on polygonal meshes. The exactly divergence-free property of virtual space preserves the mass-conservation of the system. By extending the lowest-order Raviart–Thomas element to polygonal meshes, we construct a divergence-preserving reconstructor for the discretization of the right-hand side. A rigorous a priori error analysis is developed, showing that the velocity error is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we design an adaptive mesh refinement approach and construct a residual-type a posteriori error indicator. This indicator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:This article investigates both a priori and a posteriori error estimates for a pressure-robust and divergence-free virtual element method to approximate the incompressible Brinkman problem on polygonal meshes. The exactly divergence-free property of virtual space preserves the mass-conservation of the system. By extending the lowest-order Raviart–Thomas element to polygonal meshes, we construct a divergence-preserving reconstructor for the discretization of the right-hand side. A rigorous a priori error analysis is developed, showing that the velocity error is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we design an adaptive mesh refinement approach and construct a residual-type a posteriori error indicator. This indicator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. [ABSTRACT FROM AUTHOR]
ISSN:08857474
DOI:10.1007/s10915-026-03186-y