Welcome to Lina Zhao's homepage

About me

I am an assistant professor at the Department of Mathematics, City University of Hong Kong. I am interested in developing efficient numerical schemes for partial differential equations. Currently, I am particularly interested in arbitrary Lagrangian–Eulerian Methods and machine learning for solving PDEs. A full publication list is also available at google scholar. I am open for collaboration, if you are interested in my research, please feel free to contact me (email:linazha@cityu.edu.hk) for further discussions and/or collaborations.

Open Positions

PhD Student

We are looking for a highly motivated student who wish to pursue a PhD degree in the field of numerical analysis and scientific computing. Candidates are expected to have a strong background in numerical analysis and/or coding. Outstanding applicants are encouraged to apply for the Hong Kong PHD Fellowship Scheme (HKPFS) which provides generous stipend for three years.

Postdoctoral Research Fellow:

We invite applications for a postdoc position in numerical analysis and scientific computing. The position is for one year and can be extended to another year, depending on the availability of funding. The starting date is flexible, and the position carries no teaching duties. Candidates with strong analysis and/or coding skills are encouraged to apply. Candidates with a strong publication record can be nominated for the RGC Postdoctoral Fellowship Scheme (PDFS) which provides generous financial support for three years.

Research interests

Numerical Analysis and Scientific Computing
Numerical methods for PDEs
Arbitrary Lagrangian–Eulerian Methods
Deep learning for solving PDEs
Fluid-structure interaction
Unfitted methods for muti-subdomain problem
A posteriori error estimates and adaptivity

List of Publications

Preprints(* indicates the corresponding author)

Dohyun Kim, Lina Zhao, Eric Chung and Eun-Jae Park, Pressure-robust staggered DG methods for the Navier-Stokes equations on general meshes, arXiv:2107.09226.
Lina Zhao, An optimally convergent staggered mixed method for the biharmonic problem based on the first-order system., submitted
Lina Zhao, A priori and a posteriori error analysis for the stress-velocity formulation of a quasi-Newtonian Stokes flow, submitted.
Eric Chung and Lina Zhao*, The parameter-robust DG method for fluid-structure interaction in a unified mixed formulation, submitted.
Jingyu Liu, Yang Liu and Lina Zhao*, Analysis of the staggered DG method for the quasi-Newtonian Stokes flows, submitted.
Lina Zhao, A stabilization-free HDG for linear elasticity with strongly symmetric stress on Alfeld splits, submitted.

Published

2024

Tsz Fung Yu, Eric Chung, Charles Cheung and Lina Zhao. A nonlinear upscaling method for convection-diffusion equations, accepted by Journal of Computational and Applied Mathematics.
Weifeng Qiu and Lina Zhao*, H(div)-conforming HDG methods for the stress-velocity formulation of the Stokes equations and the Navier-Stokes equations, accepted by Numerische Mathematik.

2023

Lina Zhao, A new parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress, accepted by Computers and Mathematics with Applications.
Shubin Fu, Eric Chung and Lina Zhao*, An adaptive preconditioner for three dimensional single phase compressible flow in highly heterogeneous porous media, accepted by SIAM Multiscale Modeling and Simulation.
L. A. P. Cuevas, S. Fu, E. T. Chung and L. Zhao, Convergence of the CEM-GMsFEM for compressible flow in highly heterogeneous media, accepted by Computers and Mathematics with Applications.
Shubin Fu, Eric Chung and Lina Zhao*, An efficient multiscale preconditioner for large-scale highly heterogeneous flow, accepted by SIAM Journal on Scientific Computing.
Lina Zhao and Eric Chung, Constraint energy minimizing generalized multiscale finite element method for convection diffusion equation, accepted by SIAM Multiscale Modeling and Simulation.
Lina Zhao, A priori and a posteriori error analysis of TDNNS method for linear elasticity problem under minimal regularity, accepted by Journal of Scientific Computing.
Lina Zhao and Shuyu Sun, A strongly mass conservative method for the coupled Brinkman-Darcy flow and transport, arXiv:2112.05943, accepted by SIAM Journal on Scientific Computing.

2022

Lina Zhao, Dohyun Kim, Eun-Jae Park, and Eric Chung, Staggered DG method with small edges for Darcy flows in fractured porous media, Journal of Scientific Computing, 90 (2022).
Lina Zhao, Analysis of a mixed DG method for stress-velocity formulation of the Stokes equations, Journal of Scientific Computing, 92 (2022).
Lina Zhao, Eun-Jae Park and Wonjong Kim, A novel staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: a priori and a posteriori analysis, Computers and Mathematics with Applications, 117 (2022), pp. 216-228.
Shubin Fu, Eric Chung and Lina Zhao*, Generalized multiscale finite element method for highly heterogeneous compressible flow, accepted by SIAM Multiscale Modeling and Simulation.
Lina Zhao and Eun-Jae Park, A staggered discontinuous Galerkin method for quasi-linear second order elliptic problems of nonmonotone type, Computational Methods in Applied Mathematics, 2022.
Lina Zhao, A Robin-type domain decomposition method for a novel mixed-type DG method for the coupled Stokes-Darcy problem, arXiv:2109.14825, accepted by SIAM Journal on Scientific Computing.
Lina Zhao, Eric Chung and Eun-Jae Park, A locking free staggered DG method for the Biot system of poroelasticity on general polygonal meshes, arXiv:2107.09226, accepted by IMA Journal of Numerical Analysis.
Lina Zhao and Eric Chung, Adaptive staggered DG method for Darcy flows in fractured porous media, arXiv:2006.05294, accepted by Computational Geosciences.
Lina Zhao, Eun-Jae Park and Eric Chung, A pressure robust staggered discontinuous Galerkin method for the Stokes equations, arXiv:2007.00298, accepted by Computers and Mathematics with Applications.

2021

Lina Zhao, Ming Fai Lam, and Eric Chung, A uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem , Communications on Applied Mathematics and Computation, 2021.
Lina Zhao, Eric Chung, Eun-Jae Park, and Guanyu Zhou, Staggered DG method for coupling of the Stokes and Darcy-Forchheimer problems, SIAM Journal on Numerical Analysis, 59 (2021), pp. 1–31.
Eric Chung, Hyea-Hyun Kim, Ming-Fai Lam and Lina Zhao, Learning adaptive coarse spaces of BDDC algorithms for stochastic elliptic problems with oscillatory and high contrast coefficients, Mathematical and Computational Applications, 26 (2021).
Yiran Wang, Eric Chung and Lina Zhao*, Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations, Mathematics and Computers in Simulation, 188 (2021), pp. 455-475.
Dohyun Kim, Lina Zhao and Eun-Jae Park, Review and Efficient Implementation of Staggered DG methods on Polygonal Meshes, J. Korean Soc. Ind. Appl. Math., 25 (2021), pp. 66-81.

2020

Lina Zhao, Eun-Jae park, and Eric Chung, Staggered discontinuous Galerkin methods for the Helmholtz equations with large wave number, Computers and Mathematics with Applications, 80 (2020), pp. 2676-2690.
Dohyun Kim, Lina Zhao, and Eun-Jae Park, Staggered DG methods for the pseudostress-velocity formulation of the Stokes equations on general meshes, SIAM J. Sci. Comput., 42 (2020), pp. A2537-A2560.
Lina Zhao and Eun-Jae Park, A staggered cell-centered DG method for linear elasticity on polygonal meshes, SIAM J. Sci. Comput., 42 (2020), pp. A2158-A2181.
Lina Zhao and Eric T. Chung, An analysis of the NLMC upscaling method for high contrast problems, Journal of Computational and Applied Mathematics, 367 (2020).
Lina Zhao and Eun-Jae Park, A lowest-order staggered DG method for the coupled Stokes-Darcy problem, IMA Journal of Numerical Analysis, 40 (2020), pp. 2871-2897.
Lina Zhao and Eun-Jae Park, A new hybrid staggered discontinuous Galerkin method on general meshes, Journal of Scientific Computing, 82 (2020), 12.
Lina Zhao, Eric Chung and Ming Fai Lam, A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits, Computer Methods in Applied Mechanics and Engineering, 364 (2020).

2019

Lina Zhao, Eun-Jae Park and Dong-wook Shin, A staggered DG method of minimal dimension for the Stokes equations on general meshes, Computer Methods in Applied Mechanics and Engineering, 345 (2019), pp. 854–875.
Lina Zhao and Eun-Jae Park, A priori and a posteriori error analysis of a staggered discontinuous Galerkin method for convection dominant diffusion equations, Journal of Computational and Applied Mathematics, 346 (2019), pp. 63–83.

2018

Lina Zhao and Eun-Jae Park, A staggered discontinuous Galerkin method of minimal dimension on quadrilateral and polygonal meshes, SIAM Journal on Scientific Computing, 40 (2018), pp. A2543–A2567.
Eric T. Chung, Eun-Jae Park and Lina Zhao, Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method, Journal of Scientific Computing, 75 (2018), pp. 1079–1101.
Lina Zhao and Eun-Jae Park, Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations, Computers and Mathematics with Applications, 5 (2018), pp. 4115–4134.