Zuodong Wang (王作栋)

PhD in Numerical Analysis for Partial Differential Equations (PDEs)
zuodong.wang[ατ]inria.fr
Ecole Nationale des Ponts et Chaussées (ENPC-CERMICS)
French Institute for Research in Numerical Science and Technology (INRIA - SERENA)

Welcome to my academic webpage!

About me

I am a doctor in numerical analysis under the direction of Alexandre Ern, Zhaonan Dong at CERMICS, Ecole Nationale des Ponts et Chaussées, Institut Polytechnique de Paris and SERENA team, Inria Centre de Paris. As an applied mathematician, I am mainly interested in design, test and analyze efficient numerical schemes for PDEs. My work mainly focus on structure-preserving schemes for nonlinear PDEs, including hyperbolic conservation laws, PDEs with stiff sourse, and nonlinear parabolic problems.

As a guy with diplôme d'ingénieur (engineer degree in French), I am also interested in 1) the implementation with C++, Python, Matlab and Julia(currently using). 2) Physics-related mathematical modeling.

I am currently speaking Chinese, English, French and Japanese (Duolingo level).

Research interests

  • Mathematical aspects:

    •        -    Hyperbolic Conservation Laws
           -    Semi-linear Parabolic problems
           -    PDEs with stiff sourse term
           -    Invariant Domain Preserving schemes
           -    Asymptotic Preserving schemes
           -    A posteriori error analysis for linear problems

  • Application aspects:

    •        -    Fluid Mechanics
           -    Neutron Transport
           -    Phase Field model
           -    Wave equation
           -    Adaptive algorithm

    Publications and preprints

    [7] - [Preprint] A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
    - 2025 Z. Dong, E.H. Georgoulis, L. Mascotto and Z. Wang - [link]

    [6] - A bound-preserving scheme for the Allen-Cahn equation
    - Computers and Mathematics with Applications, 2025 Z. Dong, A. Ern and Z. Wang - [link]

    [5] - [Preprint] A priori and a posteriori error estimates of a DG-CG method for the wave equation in second order formulation
    - 2024 Z. Dong, L. Mascotto and Z. Wang - [link]

    [4] - Mass conservative limiting and applications to the approximation of the steady-state radiation transport equations
    - Journal of Computational Physics, 2025 - J.-L. Guermond and Z. Wang - [link]

    [3] - Asymptotic and invariant-domain preserving schemes for scalar conservation equations with stiff source terms and multiple equilibrium points
    - Journal of Scientific Computing, 2024 - A. Ern, J.-L. Guermond and Z. Wang - [link]

    [2] - Hybrid high-order methods for elliptic PDEs on curved and complicated domains
    - 13th ICOSAHOM 2020/2021 Conference Proceeding, 2022 - Z. Dong and Z. Wang - [link]

    [1] - The Proof of 2n Circle Arrangement Conjecture
    - Pure Mathematics, 2017 - Z. Wang - [link]

    Talks

    hp-version a priori error estimates of a DG-CG method for the linear wave equation
    30th Biennial Conference on Numerical Analysis - Glasgow (UK) - 2025 - [slides]
    Asymptotic-preserving and invariant-domain preserving schemes for scalar hyperbolic conservation laws with stiff source term
    International Conference on Applied Mathematics (ICAM) - Hongkong (China) - 2024 - [slides]
    The 6th SIAM Texas-Louisiana Sectional Meeting (SIAM TX-LA) - Lafayette (USA) - 2023 - [slides]
    Monotonicity, sonic points and convergence of a stabilized FEM scheme for hyperbolic conservation laws
    Finite Element Rodeo - Houston (USA) - 2024 - [slides]

    Experiences

  • Internships:

    •        -    Testing some advanced numerical methods for hyperbolic, parabolic and elliptic PDEs.- [report]
                 SERENA team, INRIA, paris (France), 2022/10 - 2023/04.
           -    Analysis of an invariant-domain-preserving scheme for conservation laws and hyperbolic systems.- [report]
                 SERENA team, INRIA, paris (France), 2022/05 - 2022/09.
           -    Hybrid high-order method for elliptic PDEs on curved and complicated domains.- [report]
                 SERENA team, INRIA, paris (France), 2021/06 - 2021/09.


  • Visiting scholar:

    •        -    Design, analyse and test Invariant-domain-preserving schemes for hyperbolic problems.
                 Mathematical Departement, Texas A&M University, College Station (USA), September 2023 - May 2024.

    Teaching

  • Spring semester 2025 - Université Paris-Dauphine-PSL:

    •              2st year of Bachelor's degree in mathematics
                 Course : Algebra 4 and numerical methods
                 Teaching assistant: correct exercises


  • Spring semester 2024 - Texas A&M University:

    •              1st year of Bachelor's degree in engineering
                 Course : Explorations in Mathematics
                 Instructor: give lectures, correct exercises, organize exams