- Continuous and Discontinuous Galerkin Finite Element Methods
- Numerical Solutions of Stochastic Ordinary and Partial Differential Equations
- Adaptive Methods and Fast Solvers
- Phase Field and Level Set Methods for Moving Interface Problems
- Multiphase Flow and Poroelasticity
- Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise
(with X. Feng and Y. Zhang), submitted, arxiv.org/pdf/1811.05028.pdf.
- Analysis of the Morley element for the Cahn-Hilliard equation and the Hele-Shaw flow
(with S. Wu), submitted, arxiv.org/pdf/1808.08581.pdf.
- Analysis of novel adaptive two-grid finite element algorithms for linear and nonlinear problems
- Energy conserving Galerkin approximation of two dimensional wave
equations with random coefficients
(with C. Chou and D. Xiu). Journal of Computational Physics, accepted, doi.org/10.1016/j.jcp.2018.12.018.
- Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation
Journal of Scientific Computing, accepted, arxiv.org/pdf/1712.01338.pdf.
- On the stability and accuracy of partially and fully implicit schemes for phase field modeling
(with J. Xu, S. Wu and A. Bousquet). Computer Methods in Applied Mechanics and Engineering, 345: 826-853, 2019.
- Analysis of a multiphysics finite element method for a poroelasticity model
(with X. Feng and Z. Ge). IMA Journal of Numerical Analysis, 38(1): 330-359, 2018.
- Finite element methods for the stochastic Allen-Cahn equation with gradient-type multiplicative noises
(with X. Feng and Y. Zhang). SIAM Journal on Numerical Analysis, 55(1): 194-216, 2017.
- Analysis of mixed interior penalty discontinuous Galerkin methods
for the Cahn-Hilliard equation and the Hele-Shaw flow
(with X. Feng and Y. Xing). SIAM Journal on Numerical Analysis, 54(2): 825-847, 2016.
- Analysis of interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow
(with X. Feng). IMA Journal of Numerical Analysis, 35(4): 1622-1651, 2015.
- Finite element approximations of the stochastic mean curvature flow of planar curves of graphs
(with X. Feng and A. Prohl). Stochastic Partial Differential Equations: Analysis and Computations, 2(1): 54-83, 2014.
- Numerical methods for deterministic and stochastic phase
field models of phase transition and related geometric flows