Zheng "Leslie" Chen's Research Page

Research Topics

1) High order numerical methods: Discontinuous Galerkin finite element methods, Spectral methods, etc;

2) Numerical methods for kinetic equations;

3) Post-processing techiniques;

4) Numerical methods for fractional differential equations

5) Machine learning, Neural network

6) Numerical methods for uncertainty quantification;

7) Multiscale Computational Methods;

Recent Publications

L. Mu and Z. Chen, A New WENO Weak Galerkin Finite Element Method for Time Dependent Hyperbolic Equations, Applied Numerical Mathematics (2020), in press. link

M. P. Laiu, Z. Chen and C. D. Hauck, A fast implicit solver for semiconductor models in one space dimension, Journal of Computational Physics (2020): 109567. link

Z. Chen and C. D. Hauck, Multiscale convergence properties for spectral approximations of a model kinetic equation, Mathematics of Computation 88.319 (2019): 2257-2293. link

Z. Chen, L. Liu and L. Mu, DG-IMEX Stochastic Galerkin schemes for LinearTransport Equation with Random Inputs and Diffusive Scalings, Journal of Scientific Computing (2017), 73(2), 566-592. link

H. Huang, Z. Chen, J. Li and J. Yan, Direct discontinuous Galerkin method and its variations for second order elliptic equations, Journal of Scientific Computing (2017), 70(2), 744-765. link

Z. Chen, H. Huang and J. Yan, Third order Maximum-Principle-Satisfying Direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes, Journal of Computational Physics, v308(2016), pp.198-217. link

Y. Chen, Z. Chen, Y. Cheng, A. Gillman and F. Li, Study of Discrete Scattering Operators for Some Linear Kinetic Models, S. C. Brenner (Editor), In Topics in Numerical Partial Differential Equations and Scientific Computing, Springer-Verlag New York, IMA Volumes in Mathematics and its Applications, Vol. 160(2016), pp.99-136. link

Z. Chen and C.-W. Shu, Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities, Journal of Scientific Computing, v65(2015), pp.1145-1165. link

Z. Chen and C.-W. Shu, Recovering exponential accuracy from collocation point values of smooth functions with end-point singularities, Journal of Computational and Applied Mathematics, v265 (2014), pp.83-95. link