1. 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]

2. 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]

3. 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]

4. 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]

5. L. Rebholz, S. Wise and M. Xiao, Penalty-Projection Schemes for the Cahn-Hilliard NavierStokes 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]

6. 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]

7. 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]

8. 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]

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

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

11.  M. Xiao, An efficient nonlinear solver for steady MHD based on algebraic splitting, International Journal of Numerical Analysis and Modeling, to appear.