M. Mohebujjaman, M. Xiao and C. Zhang, A simple-to-implement nonlinear preconditioning of Newton's method for solving the steady Navier-Stokes equations, submitted. [Arxiv] 

S. Pollock, L. Rebholz, X. Tu and M. Xiao, Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence, Journal of Scientific Computing, 104, 25, 2025. [Link][Arxiv]

M. Mohebujjaman, J. Miranda, Md. A. Al Mahbub and M. Xiao, An Efficient and Accurate Penalty-projection Eddy Viscosity Algorithm for Stochastic Magnetohydrodynamic Flow Problems, Journal of Scientific Computing, 101(1):2, 2024. [Link][Arxiv]

M. Xiao, Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier-Stokes equations, Numerical Methods for Partial Differential Equations, 39(4), 3089-3107, 2023. [Link] [Arxiv]

L. Rebholz and M. Xiao, The effect of Anderson acceleration on the convergence order of nonlinear solvers, Journal of Scientific Computing, 96:34, 2023. [Link]

L. Rebholz, D. Vargun and  M. Xiao, Enabling fast convergence of the iterated penalty Picard iteration with O(1) penalty parameter for incompressible Navier-Stokes via Anderson acceleration, Computer Methods in Applied Mechanics and Engineering, 387, 114178, 2021. [Link] [Arxiv]

S. Pollock, L. Rebholz and M. Xiao, Acceleration of nonlinear solvers for natural convection problems, Journal of Numerical Mathematics,29(4), 323-341, 2021. [Link] [Arxiv] 

M. Xiao, An efficient nonlinear solver for steady MHD based on algebraic splitting, International Journal on Numerical Analysis and Modeling, 18, 674-689, 2021. [Link]

L. Rebholz, A. Viguerie and M. Xiao, Analysis of Algebraic Chorin-Temam splitting for incompressible Navier-Stokes equations and comparison to Yosida methods, Journal of Computational and Applied Mathematics, 365, 112366, 2020. [Link] 

C. Evans, S. Pollock, L. Rebholz and M. Xiao, A proof that Anderson acceleration increases the convergence rate in linearly converging fixed point methods (but not in quadratically converging ones), SIAM Journal on Numerical Analysis, 58(1), 788-810, 2020. [Link] [Arxiv]

S. Pollock, L. Rebholz and M. Xiao, Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, 57(2), 615- 637, 2019. [Link] [Download]

L. Rebholz, A.Viguerie and M. Xiao, Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations, Mathematics of Computation, 88, 1533- 1557, 2019. [Link]  [Download]

A. Viguerie and M. Xiao, Effective Chorin-Temam Algebraic Splitting Schemes for the Steady Navier-Stokes Equations, Numerical Methods for Partial Differential Equations, 35(2), 805-829, 2018. [Link]  [Download]

L. Rebholz, S. Wise and M. Xiao, Penalty-Projection Schemes for the Cahn-Hilliard Navier- Stokes Diffuse Interface Model of Two Phase Flow, and their Connection to Divergence-Free Coupled Schemes, International Journal on Numerical Analysis and Modeling, 4, 649-676, 2018. [Link]  [Download]

L. Rebholz and M. Xiao, Improved accuracy in algebraic splitting methods for Navier-Stokes equations, SIAM Journal on Scientific Computing, 39(4), A1489-A1513, 2017. [Link]  [Download]

M. Akbas, M. Mohebujjaman, L. Rebholz, M. Xiao, High order algebraic splitting for magnetohydrodynamics simulation, Journal of Computational and Applied Mathematics, 321, 128-142, 2017. [Link]  [Download]

T. Heister, L. Rebholz and M. Xiao, Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems, Journal of Mathematical Analysis and Applications, 438(1), 507-513, 2016. [Link]  [Download]

L. Rebholz and M. Xiao, On reducing the splitting error in Yosida methods for the Navier-Stokes equations with grad-div stabilization, Computer Methods in Applied Mechanics and Engineering, 294, 259-277, 2015.  [Link] [Download]