Lixiu Dong
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Lixiu Dong has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Cheng Wang
Department of Mathematics, The University of Massachusetts, North Dartmouth, USA
1 shared publication - Juan Zhang
School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China
1 shared publication - Maoqin Yuan
School of Mathematics, Physics and Artificial Intelligence, China University of Petroleum-Beijing at Karamay, Karamay 834000, China
1 shared publication - Mingyang Li
School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
1 shared publication - Zhengru Zhang
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences Beijing Normal University Beijing People's Republic of China
1 shared publication
Latest Publications
- Open Access
An Energy-Stable Variable-Step SAV Finite Element Method for a Droplet Thin-Film Coarsening Model with a Lennard–Jones Singular Potential
We develop an energy-stable variable-step BDF2-based scalar auxiliary variable (SAV) finite element scheme for a droplet thin-film coarsening model with a Lennard–Jones singular potential. The method uses continuous piecewise linear finite elements in space and retains the original linear SAV update. We prove discrete mass conservation, modified-energy decay under an admissible step-ratio condition, and solvability of the coupled algebraic system. A Sherman–Morrison realization exploits the rank-one coupling and reduces each accepted time step to two solves with the same sparse base matrix. Numerical experiments assess temporal and spatial convergence, SAV-shift sensitivity, two-droplet mesh dependence, long-time coarsening, and solver efficiency. The film-height variable exhibits second-order temporal convergence and the expected spatial rates, whereas the auxiliary variable is first-order accurate; the consistency audit shows no hidden cancellation. The computations also verify mass conservation, modified-energy decay, positive film heights in the reported runs, and the efficiency of the sparse solver.
Open AccessAn Energy-Stable Variable-Step SAV Finite Element Method for a Droplet Thin-Film Coarsening Model with a Lennard–Jones Singular Potential
We develop an energy-stable variable-step BDF2-based scalar auxiliary variable (SAV) finite element scheme for a droplet thin-film coarsening model with a Lennard–Jones singular potential. The method uses continuous piecewise linear finite elements in space and retains the original linear SAV update. We prove discrete mass conservation, modified-energy decay under an admissible step-ratio condition, and solvability of the coupled algebraic system. A Sherman–Morrison realization exploits the rank-one coupling and reduces each accepted time step to two solves with the same sparse base matrix. Numerical experiments assess temporal and spatial convergence, SAV-shift sensitivity, two-droplet mesh dependence, long-time coarsening, and solver efficiency. The film-height variable exhibits second-order temporal convergence and the expected spatial rates, whereas the auxiliary variable is first-order accurate; the consistency audit shows no hidden cancellation. The computations also verify mass conservation, modified-energy decay, positive film heights in the reported runs, and the efficiency of the sparse solver.
- Open Access
A positivity-preserving, second-order energy stable and convergent numerical scheme for a ternary system of macromolecular microsphere composite hydrogels
A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy potential. This numerical scheme with energy stability is based on the Backward Differentiation Formula(BDF) method in time derivation combining with Douglas-Dupont regularization term, combined the finite difference method in space. We provide a theoretical justification of positivity-preserving property for all the singular terms, i.e., not only the two phase variables are always between $0$ and $1$, but also the sum of the two phase variables is between $0$ and $1$, at a point-wise level. In addition, an optimal rate convergence analysis is provided in this paper, in which a higher order asymptotic expansion of the numerical solution, the rough error estimate and refined error estimate techniques have to be included to accomplish such an analysis. This paper will be the first to combine the following theoretical properties for a second order accurate numerical scheme for the ternary MMC system: (i) unique solvability and positivity-preserving property; (ii) energy stability; (iii) and optimal rate convergence. A few numerical results are also presented.Open AccessA positivity-preserving, second-order energy stable and convergent numerical scheme for a ternary system of macromolecular microsphere composite hydrogels
A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy potential. This numerical scheme with energy stability is based on the Backward Differentiation Formula(BDF) method in time derivation combining with Douglas-Dupont regularization term, combined the finite difference method in space. We provide a theoretical justification of positivity-preserving property for all the singular terms, i.e., not only the two phase variables are always between $0$ and $1$, but also the sum of the two phase variables is between $0$ and $1$, at a point-wise level. In addition, an optimal rate convergence analysis is provided in this paper, in which a higher order asymptotic expansion of the numerical solution, the rough error estimate and refined error estimate techniques have to be included to accomplish such an analysis. This paper will be the first to combine the following theoretical properties for a second order accurate numerical scheme for the ternary MMC system: (i) unique solvability and positivity-preserving property; (ii) energy stability; (iii) and optimal rate convergence. A few numerical results are also presented.