In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and ...In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and exact divergence-free.By virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete scheme.The con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the pressure.Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.展开更多
文摘In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and exact divergence-free.By virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete scheme.The con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the pressure.Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.
