For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two no...For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses, and gave the detailed convergence analysis. In this paper, we focus on the convergence analysis of this corrected Uzawa algorithm, some inaccuracies in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] are pointed out, and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.展开更多
An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method.The velocity solved by the presented algorithm is weakly divergence-free,which is different from the ...An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method.The velocity solved by the presented algorithm is weakly divergence-free,which is different from the one solved by the common Uzawa method.Besides,an optimal relaxation parameter of the presented algorithm is provided.展开更多
In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that unde...In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that under given proper preconditioners,Uzawa algorithm is convergent for the stablization system.Bounds for the iteration error are provided.We show numerically that Uzawa algorithm is convergent as well for the stabilization systems when it is used in the steady-state Navier-Stokes problem(cf.[6]).展开更多
基金Supported by the National Natural Science Foundation of China(11201422)the Natural Science Foundation of Zhejiang Province(Y6110639,LQ12A01017)
文摘For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses, and gave the detailed convergence analysis. In this paper, we focus on the convergence analysis of this corrected Uzawa algorithm, some inaccuracies in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] are pointed out, and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.
基金Project supported by the National Natural Science Foundation of China(No.11861067)。
文摘An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method.The velocity solved by the presented algorithm is weakly divergence-free,which is different from the one solved by the common Uzawa method.Besides,an optimal relaxation parameter of the presented algorithm is provided.
文摘In this paper,we consider the so-called "inexact Uzawa" algorithm applied to the unstable Navier-Stokes problem.We use stabilization matrix to stabilize the unstable system and proved theoretically that under given proper preconditioners,Uzawa algorithm is convergent for the stablization system.Bounds for the iteration error are provided.We show numerically that Uzawa algorithm is convergent as well for the stabilization systems when it is used in the steady-state Navier-Stokes problem(cf.[6]).