- 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), submitted, arxiv.org/pdf/1805.04183.pdf.
- 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, accepted, 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