- 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
- 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), submitted, arxiv.org/pdf/1805.04183.pdf.
- Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation
- On the stability and accuracy of partially and fully implicit schemes for phase field modeling
(with J. Xu, S. Wu and A. Bousquet), submitted, arxiv.org/pdf/1604.05402.pdf .
- Multiphysics finite element methods 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