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  1. Article

    Correction to : An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-Component Chemically Reacting Flows

    Jie Du, Yong Liu, Yang Yang in Journal of Scientific Computing (2024)

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    An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows

    This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations a...

    Jie Du, Yong Liu, Yang Yang in Journal of Scientific Computing (2023)

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    Article

    High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations

    In this paper, we apply high-order finite difference (FD) schemes for multispecies and multireaction detonations (MMD). In MMD, the density and pressure are positive and the mass fraction of the ith species in th...

    Jie Du, Yang Yang in Communications on Applied Mathematics and Computation (2023)

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    Article

    Maximum-Principle-Preserving Local Discontinuous Galerkin Methods for Allen-Cahn Equations

    In this paper, we study the classical Allen-Cahn equations and investigate the maximum-principle-preserving (MPP) techniques. The Allen-Cahn equation has been widely used in mathematical models for problems in...

    Jie Du, Eric Chung, Yang Yang in Communications on Applied Mathematics and Computation (2022)

  5. Article

    Polynomial super representations of \(U_{q}^{\mathrm{res}}(\mathfrak {gl}_{m|n})\) at roots of unity

    As a homomorphic image of the hyperalgebra \(U_{q,R}(m|n)\)Uq,R(m|n) associated with the quantum linear supergroup \(U_{\varvec{\upsilon }}(\mathfrak {gl}_{m|n})\)Uυ(glm|n), we first give a presentation for the q

    Jie Du, Yanan Lin, Zhongguo Zhou in Journal of Algebraic Combinatorics (2020)

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    Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlap** meshes

    Local discontinuous Galerkin (LDG) methods are popular for convection–diffusion equations. In LDG methods, we introduce an auxiliary variable p to represent the derivative of the primary variable u, and solve the...

    Jie Du, Yang Yang, Eric Chung in BIT Numerical Mathematics (2019)

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    Article

    An Adaptive Staggered Discontinuous Galerkin Method for the Steady State Convection–Diffusion Equation

    Staggered grid techniques have been applied successfully to many problems. A distinctive advantage is that physical laws arising from the corresponding partial differential equations are automatically preserve...

    Jie Du, Eric Chung in Journal of Scientific Computing (2018)

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    Article

    Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations

    In this paper, we present a discontinuous Galerkin method with staggered hybridization to discretize a class of nonlinear Stokes equations in two dimensions. The utilization of staggered hybridization is new a...

    Jie Du, Eric T. Chung, Ming Fai Lam, **ao-** Wang in Journal of Scientific Computing (2018)

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    Article

    Local and global methods in representations of Hecke algebras

    This paper aims at develo** a “local-global” approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applicat...

    Jie Du, Brian J. Parshall, Leonard L. Scott in Science China Mathematics (2018)

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    Article

    An Adaptive SDG Method for the Stokes System

    Staggered grid techniques are attractive ideas for flow problems due to their more enhanced conservation properties. Recently, a staggered discontinuous Galerkin method is developed for the Stokes system. This...

    Eric T. Chung, Jie Du, Man Chun Yuen in Journal of Scientific Computing (2017)

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    Article

    Small Representations for Affine q-Schur Algebras

    When the parameter q ∈ ...

    Jie Du, Qiang Fu in Algebras and Representation Theory (2016)

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    Article

    Canonical bases for the quantum supergroups \({\mathbf {U}}(\mathfrak {gl}_{m|n})\)

    We give a combinatorial construction for the canonical bases of the \(\pm \) ...

    Jie Du, Haixia Gu in Mathematische Zeitschrift (2015)

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    Article

    A modified BLM approach to quantum affine \({\mathfrak{gl}_n}\)

    We introduce a spanning set of Beilinson–Lusztig–MacPherson type, {A(j, r)}A,j, for affine quantum Schur algebras $${{{\boldsymbol{\ma...

    Jie Du, Qiang Fu in Mathematische Zeitschrift (2010)

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    Chapter

    Quantum \(\mathfrak{gl}_n,\) q-Schur Algebras and Their Infinite/Infinitesimal Counterparts

    We present a survey of recent developments of the Beilinson–Lusztig–MacPherson approach in the study of quantum \({\mathfrak{g}\mathfrak{l}}_{n}\) ...

    Jie Du, Qiang Fu in Representation Theory of Algebraic Groups and Quantum Groups (2010)

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    Article

    Finite-Dimensional Algebras and Standard Systems

    We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite-dimensional algebra to be quasi-hereditary is...

    Jie Du in Algebras and Representation Theory (2003)

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    Article

    Ariki-Koike algebras with semisimple bottoms

    Jie Du, Hebing Rui in Mathematische Zeitschrift (2000)

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    Article

    Integral Schur algebras forGL 2

    The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,

    Jie Du in manuscripta mathematica (1992)

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    Article

    The modular representation theory ofq-Schur algebras. II

    Jie Du in Mathematische Zeitschrift (1991)