28 citations · 33 across the 7 of their papers we have counts for
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Error estimates for the scalar auxiliary variable (SAV) scheme to the Cahn-Hilliard equation
Shu Ma, Weifeng Qiu, Xiaofeng Yang
The optimal error estimate that depending only on the polynomial degree of is established for the temporal semi-discrete scheme of the Cahn-Hilliard equation, w…
Optimal analysis of finite element methods for the stochastic Stokes equations
Buyang Li, Shu Ma, Weiwei Sun
Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-…
A semi-implicit low-regularity integrator for Navier-Stokes equations
Buyang Li, Shu Ma, Katharina Schratz
A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrato…
Analysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data
Buyang Li, Shu Ma, Yuki Ueda
First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with initial dat…
A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
Buyang Li, Shu Ma
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic…
High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation
Xiaobing Feng, Buyang Li, Shu Ma
A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable formu…
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations
Xiaobing Feng, Hailiang Liu, Shu Ma
In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schrödinger equations. The proposed schemes all satisfy both mass conservation and e…