Research

## Changhui Tan

I am a postdoctoral research associate in CSCAMM and Department of Mathematics, University of Maryland.

Tuesday, 12 May 2020 11:19

### MATH724 Differential Equations II Lecture March 24, 2020

Tuesday, 07 April 2020 14:21

### Global regularity for a 1D Euler-alignment system with misalignment

• This is a joint work with Qianyun Miao and Liutang Xue.
• The preprint is available on arXiv:2004.03652.
Saturday, 29 February 2020 15:07

### The Monolithic Arbitrary Lagrangian-Eulerian (ALE) Finite Element Analysis of Moving Interface Problems

#### Speaker: Rihui Lan (University of Nevada, Las Vegas)

In this talk, two different moving interface problems are studied by different arbitrary Lagrangian-Eulerian (ALE) finite element methods. For the transient Stokes/parabolic coupling with jump coefficients—a linearized fluid-structure interaction (FSI) problem, a novel $$H^1$$-projection is defined to account for the mesh motion. The well-posedness and optimal convergence properties in both the energy norm and $$L^2$$ norm are analyzed for this mixed-type $$H^1$$-projection, with which the stability and optimal error estimate in the energy norm are derived for both semi- and fully discrete mixed finite element approximations to the Stokes/parabolic interface problem. For the parabolic/mixed parabolic moving interface problem with jump coefficients, a stable Stokes-pair mixed FEM within a specific stabilization technique and a novel ALE time-difference scheme are developed to discretize this interface problem in both semi- and fully discrete fashion, for which the stability and optimal error estimate analyses are conducted.

Time: March 27, 2020 2:30pm-3:30pm
Location: LC317R
Host: Lili Ju

Tuesday, 11 February 2020 16:48

### Efficient, positive, and energy stable schemes for Poisson-Nernst-Planck systems

#### Speaker: Hailiang Liu (Iowa State University)

We are concerned with positive and energy-dissipating schemes for solving the time-dependent system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling of biological membrane channels and semiconductor devices. As a gradient flow in density space, this strongly coupled system of nonlinear equations can take long time evolution to reach steady states. Hence, designing efficient and stable methods is highly desirable. In this talk we shall present a class of methods with structure-preserving properties for the PNP system, and review advances around related models such as the quantum diffusion equation.

Time: February 21, 2020 2:30pm-3:30pm
Location: LC317R
Host: Changhui Tan

Wednesday, 29 January 2020 22:37

### On a class of new nonlocal traffic flow models with look-ahead rules

• This is a joint work with Yi Sun.
• The preprint is available on arXiv:2001.10017.
Friday, 24 January 2020 22:32

### Mathematical and numerical analysis to variable-order mobile-immobile time-fractional diffusion equations

#### Speaker: Xiangcheng Zheng (University of South Carolina)

We proved the wellposedness of variable-order mobile-immobile time-fractional diffusion equations and the regularity of their solutions. Optimal-order finite element approximation was presented and analyzed. Numerical experiments were carried out for demonstration.

Time: January 31, 2020 2:30pm-3:30pm
Location: LC317R

Wednesday, 15 January 2020 16:31

### Lagrangian Front Tracking and Applications to Conservation Law, Fluid Mixing, and Phase Transition Problems

#### Speaker: Xiaolin Li (Stony Brook University)

In this talk, I will review the history of the Lagrangian front tracking method and the computational platform built on this methodology. I will review the front tracking in the study of fluid interface instabilities, including Rayleigh-Taylor instability, Richtmyer Meshkov instability and fluid mixing induced by these instabilities. I will also introduce a fully conservative front tracking scheme and its application in the phase transition problem.

Time: March 20, 2020 2:30pm-3:30pm
Location: LC317R
Host: Xinfeng Liu

Thursday, 09 January 2020 09:04

### Traveling Wave of Gray-Scott System: Results and Perspective

#### Speaker: Yuanwei Qi (University of Central Florida)

In this talk, I shall report some recent progress on the existence and multiplicity of traveling waves to one of the most important models in Turing Pattern Formation. In addition, I shall pose some questions which are wide open which demand new ideas and fresh approaches. This is a joint-work with Xinfu Chen et al.

Time: January 17, 2020 2:30pm-3:30pm
Location: LC317R
Host: Changhui Tan

Tuesday, 03 December 2019 17:28

### ACM Seminar Schedule

Regular seminar talk time and location: Fridays 2:30pm-3:30pm @ LC 317 R.

#### Spring 2020

 January 17 Yuanwei Qi (University of Central Florida) Host: Changhui Tan Title: Traveling Wave of Gray-Scott System: Results and Perspective January 31 Xiangcheng Zheng (University of South Carolina) Math Graduate Student Title: Mathematical and numerical analysis to variable-order mobile-immobile time-fractional diffusion equations February 21 Hailiang Liu (Iowa State University) Host: Changhui Tan Title: Efficient, positive, and energy stable schemes for Poisson-Nernst-Planck systems March 20 Xiaolin Li (Stony Brook University) Host: Xinfeng Liu (Postponed) Title: Lagrangian Front Tracking and Applications to Conservation Law, Fluid Mixing, and Phase Transition Problems March 27 Rihui Lan (University of Nevada, Las Vegas) Host: Lili Ju (Postponed) Title: The Monolithic Arbitrary Lagrangian-Eulerian (ALE) Finite Element Analysis of Moving Interface Problems

#### 2019 and before

The schedule can be found HERE and HERE.

Monday, 23 September 2019 09:01

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