# Research

## Research Interests

• Data-driven modeling of systems driven by (stochastic) differential equations

• Numerical simulation of stochastic differential equations and rare events

• Finite Element Method, discontinuous Galerkin method, Virtual Element Method

• Interface problems and coupling mathematical models arising from applications

## Publications

### Preprints

1. Yuan Chen, Yulong Xing. Optimal Error Estimates of Ultra-weak Discontinuous Galerkin Methods with Generalized Numerical Fluxes for Multi-dimensional Convection-Diffusion and Biharmonic Equations., (2023+), submitted.

2. Victor Churchill, Yuan Chen, Zhongshu Xu, and Dongbin Xiu. DNN Modeling of Partial Differential Equations with Incomplete Data., (2023+), submitted. [SSRN]

3. Yuan Chen, Songming Hou, and Xu Zhang. Semi and Fully Discrete Analysis for An Immersed Finite Element Method for Elastodynamic Interface Problems., (2023+), submitted.

4. Yuan Chen, Xu Zhang. Solving Navier-Stokes Interface Problems with Fixed and Moving Interfaces on Unfitted Meshes, (2023+), submitted.

5. Yuan Chen, Xu Zhang. A High-order Immersed $$C^0$$ Interior Penalty Method for Biharmonic Interface Problems., (2023+), preprint.

### Journal Publications

1. Yuan Chen, Xu Zhang. A $$\mathcal{P}_2$$-$$\mathcal{P}_1$$ Partially Penalized Immersed Finite Element Method for Stokes Interface Problem. International Journal of Numerical Analysis and Modeling, 18 (2021), no. 1, 120-141. [pdf]

2. Yuan Chen, Songming Hou and Xu Zhang. A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-domains and Triple Junction Points. Results in Applied Mathematics, 8 (2020), 100100. [pdf]

3. Yuan Chen, Songming Hou and Xu Zhang. An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points. Advances in Applied Mathematics and Mechanics, 11 (2019), no. 5, 1005-1021. [pdf]