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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
Yuan Chen, Dongbin Xiu. Learning Stochastic Dynamical System via Flow Map Operator, (2023+), submitted. [arXiv]
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.
Victor Churchill, Yuan Chen, Zhongshu Xu, and Dongbin Xiu. DNN Modeling of Partial Differential Equations with Incomplete Data., (2023+), submitted. [SSRN]
Yuan Chen, Songming Hou, and Xu Zhang. Semi and Fully Discrete Analysis for An Immersed Finite Element Method
for Elastodynamic Interface Problems., (2023+), submitted.
Yuan Chen, Xu Zhang. Solving Navier-Stokes Interface Problems with Fixed and Moving Interfaces on Unfitted Meshes, (2023+), submitted.
Yuan Chen, Xu Zhang. A High-order Immersed \(C^0\) Interior Penalty Method for Biharmonic Interface
Problems., (2023+), preprint.
Journal Publications
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]
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]
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]
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