A WENO algorithm for radiative transfer with resonant scattering: the time scale of the Wouthuysen-Field Coupling

I Roy, J.-M. Qiu, C.-W. Shu, and L.-Z. Fang

Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning

G.B. Jacobs and J.S. Hesthaven

IMEX evolution of scalar fields on curved backgrounds

S.R. Lau, H.P. Pfieffer, and J.S. Hesthaven

Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem

Y. Chen, J.S. Hesthaven, Y. Maday, and J. Rodriguez

Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs

Y. Xu and C.-W. Shu

Revisiting and extending interface penalties for multi-domain summation-by-parts operators

M.H. Carpenter, J. Nordstrom, and D. Gottlieb

Galerkin method for wave equations with uncertain coefficients

D Gottlieb and D Xiu

Modified Optimal Prediction and its Application to a Particle-Method Problem

A Chertock, D Gottlieb and A Solonomoff

High-order accurate thin layer approximations for time-domain electromagnetics. Part I: General metal backed coatings

S. Chun and J. S. Hesthaven

Superconvergence of Local Discontinuous Galerkin Methods for Convection-Diffusion Equations

Y. Cheng and C.-W. Shu

High Order Strong Stability Preserving Time Discretizations

S. Gottlieb, D.I. Ketcheson, and C.-W. Shu

Discontinuous Galerkin Methods: General Approach and Stability

C.-W. Shu

Numerical Boundary Conditions for the Fast Sweeping High-Order WENO Methods for Solving the Eikonal Equation

L. Huang, C.-W. Shu and M. Zhang

The WKB local discontinuous Galerkin method for the simulation of Schrodinger equation in a resonant tunneling diode

W. Wang and C.-W. Shu

A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations

J. Cheng adn C.-W. Shu

Polymorphic Nodal Elements and their Application in Discontinuous Galerkin Methods

G.J. Gassner, F. Lorcher, C.-D. Munz and J.S. Hesthaven

Local discontinuous Galerkin method for the Hunter-Saxton equation and its zero-viscosity and zero-dispersion limit

Y. Xu and C.-W. Shu

Front tracking algorithm for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic, continuous, non-smooth, and non-concave fundamental diagram

W. Chen, S.C. Wong, C.-W. Shu adn P. Zhang

Hierarchial Reconstruction for Discontinuous Galerkin Methods on Unstructured Grids with a WENO Type Linear Reconstruction

Z. Xu, Y. Liu, and C.-W. Shu

Development of Nonlinear Weighted Compact Schemes with Increasingly Higher Order Accuracy

S Zhang, S Jiang and C-W Shu

Superconvergence and Time Evolution of Discontinuous Galerkin Finite Element Solutions

Y. Cheng and C.-W. Shu

Partial Spherical Means for the 3+1 Wave Equation:Towards Face, Edge, and Corner Radiation Conditions

S Lau

Runge−Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes

J. Zhu, J. Qiu, C.-W. Shu, and M. Dumbser

An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model

Y. Xia, S.C. Wong, M. Zhang, C.-W. Shu, and W. H.K. Lam

Development of Residual Distribution Schemes for Discontinuous Galerkin Method: The Scalar Case with Linear Elements

R Abgrall and C.-W. Shu

Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hillard System

Y. Xia, Y. Xu, and C.-W. Shu

Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes

Y.-T. Zhang and C.-W. Shu

The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids

W. Wang, X. Li, and C.-W. Shu

A Second Order Discontinuous Galerkin Fast Sweeping Method for Eikonal Equations

F.Li, C.-W. Shu, Y.-T. Zhang and H. Zhao

A High-Order ENO Conservative Lagrangian Scheme for the Compressible Euler Equations

J. Cheng and C.-W. Shu

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

T Hagstrom and S Lau

Strong Stability Preserving Property of the Deferred Correction Time Discretization

Y. Liu, C.-W. Shu, and M. Zhang

The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship

Y. Lu, S.C. Wong, M. Zhang, and C.-W. Shu

A High Order WENO Scheme for a Hierarchical Size-Structured Model

J. Shen, C.-W. Shu and M. Zhang

L2 Stability Analysis of the Central Discontinuous Galerkin Method and a Comparison between the Central and Regular Discontinuous Galerkin Methods

Y. Liu, C.-W. Shu, E. Tadmor, and M. Zhang

Convergence of High Order Finite Volume Weighted Essentially Nonoscillatory Schemes and Discontinuous Galerkin Methods for Nonconvex Conservation Laws

J.-M. Qiu and C.-W. Shu

Discontinuous Galerkin Method for a Class of Elliptic Multi-Scale Problems

L. Yuan and C.-W. Shu

Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations

Y. Xia, Y. Xu, and C.-W. Shu

A Local Discontinuous Galerkin Method for the Camassa-Holm Equation

Y. Xu and C.-W. Shu

Post-Processing for the Discontinuous Galerkin Method over Non-Uniform Meshes

S. Curtis, R.M Kirby, J.K. Ryan, C.-W. Shu

Multidomain Spectral Method for the Helically Reduced Wave Equation

S. R. Lau and R.H. Price

High Order Weigthed Essentially Non-Oscillatory Schemes for Convection Dominated Problems

C.-W. Shu

High Order Well-Balanced Finite Volume WENO Schemes for Shallow Water Equation with Moving Water

S. Noelle, Y. Xing, and C.-W. Shu

Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

Y. Liu, C.-W. Shu, E. Tadmor, and M. Zhang

A Discontinuous Galerkin Finite Element Method for Time Dependent Partial Differential Equations with Higher Order Derivatives

Y. Cheng and C.-W. Shu

Efficient Time-Discretization for Local Discontinuous Galerkin Methods

Y. Xia, Y. Xu, and C.-W. Shu

Central Discontinuous Galerkin Methods on Overlapping Cells With a Non-Oscillatory Hierarchical Reconstruction

Y. Liu, C.-W. Shu, E. Tadmor, and M. Zhang

Pade-Gegenbauer Suppression of Runge Phenomenon in the Diagonal Limit of Gegenbauer Approximations

L. Lurati

An Improved Weigthed Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws

R. Borges, B. Costa, and W.S. Don

A Reactive Dynamic User Equilibrium Model for Pedestrian Flows: A Continuum Modeling Approach

L. Huang, S.C. Wong, M. Zhang, C.-W. Shu, and W.H.K. Lam

21 cm Emisson from Ionized Clouds of UV Sources in the Reionization Epoch

L.-L. Feng, J.-M. Qiu, C.-W. Shu, and L.-Z. Fang

Explicit Construction of Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Non-Smooth Flow-Density Relationship

Y. Li, S.C. Wong, M. Zhang, C.-W. Shu, and W. Chen

High Order Residual Distribution Conservative Finite Difference WENO Schemes for Convection-Diffusion Steady State Problems on Non-smooth Meshes

C.-S. Chou and C.-W. Shu

A Discontinuous Galerkin Finite Element Method for Directly Solving the Hamilton-Jacobi Equations

Y. Cheng and C.-W. Shu

Interaction of a Shock Wave with an Oblique Vortex Pair: Shock Dynamics and Mechanism of Sound Generation

S. Zhang, Y.-T. Zhang, and C.-W. Shu

Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps

J. Qiu and C.-W. Shu

Convergence towards Steady State Solutions of the Euler Equations with WENO Schemes

S. Zhang and C.-W. Shu

Multi-Domain Hybrid Spectral-WENO Methods for Hyperbolic Conservation Laws

B. Costa and W.S. Don

Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant

Z. Xu and C.-W. Shu

High Order Hybrid Central-WENO Finite Difference Scheme for Conservation Laws

B. Costa and W.S. Don

Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws

B. Costa, W.S. Don, D. Gottlieb, and R. Sendersky

A WENO Algorithm for the Radiative Transfer and Ionized Sphere at Reionization

J. Qiu, C.-W. Shu, L.-L. Feng, and L.-Z. Fang

Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations

X. Wan and G.E. Karniadakis

Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method for Nonlinear Convection-Diffusion and KdV Equations

Y. Xu and C.-W. Shu

A High Order Accurate Conservative Remapping Method on Staggered Meshes

J. Cheng and C.-W. Shu

Discontinuous Galerkin Method Based on Non-Polynomial Approximation

L. Yuan and C.-W. Shu

A Local-Structure Preserving Local Discontinuous Galerkin Method for the Laplace Equation

F. Li and C.-W. Shu

Local Discontinuous Galerkin Methods for Moment Models in Device Simulations: Performance Assessment and Two-Dimensional Results

Y. Liu and C.-W. Shu

A Domain Decomposition Method for Kinetic-Hydrodynamic Multiscale Problems in Gas Dynamics and Device Simulations Using the Discontinuous Galerkin Methods

S. Chen, W.E., Y. Liu, and C.-W. Shu

High Resolution Schemes for a Hierarchical Size-Structured Model

J. Shen, C.-W. Shu, and M. Zhang

Reduced Navier-Stokes Equations Near a Flow Boundary

M.S. Kilic, G.B. Jacobs, J.S. Hesthaven, and G. Haller

A New Approach of High Order Well-Balance Finite Volume WENO Schemes and DIscontinuous Galerkin Methods for a Class of Hyperbolic Systems with Source Terms

Y. Xing and C.-W. Shu

High Order Residual Distribution Conservative Finite Difference WENO Schemes for Steady State Problems on Non-Smooth Meshes

C.-C. Chou, and C.-W. Shu

Low-Redshift Cosmic Baryon Fluid on Large Scales: A Fully Developed Turbulence

P. He, L.-L. Feng, C.-W. Shu, and L.-Z. Fang

Demonstrating Shock Mitigation and Drag Reduced by Pulsed Energy Lines with Multi-Domain WENO

K. Kremeyer, K. Sebastian, and C.-W. Shu

Effects of Shock Waves on Rayleigh-Taylor Instabilities

Y.-T. Zhang, C.-W. Shu, and Y. Zhou

2D Semiconductor Device Simulations by WENO-Boltzmann Schemes: Efficiency, Boundary Conditions, and Comparison to Monte Carlo Methods

J.A. Carillo, I.M. Gamba, A. Majorana, and C.-W. Shu

A Weighted Essentially Non-Oscillatory Numerical Scheme for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway

S. Abarbanel, D. Gottlieb, and J.S. Hesthaven

Gappy Data: To Krig or Not To Krig

H. Gunes, S. Sirisup, and G.E. Karniadakis

A Numerical Study of the Performance ofthe Runge-Kutta Discontinuous Galerkin Method Based on Different Numerical Fluxes

J. Qiu, B.C. Khoo, and C.-W. Shu

Anti-Diffusive High-Order WENO Schemes for Hamilton-Jacobi Equations

Z. Xu and C.-W. Shu

The Next Step in Coastal Numerical Models: Spectral/hp Element Methods

C. Eskilsson, A.P. Engsig-Karup, S.J. Sherwin, J.S. Hesthaven, and L. Bergdahl

Non-Linear PML Equations for Time-Dependent Electromagnetics in Three Dimensions

S. Abarbanel, D. Gottlieb, and J.S. Hesthaven

Time-Consisten Filtering in Spectral and Spectral Element Methods

A. Kanevksy, M.H. Carpenter, and J.S. Hesthaven

Pade-Jacobi Approximants

J.S. Hesthaven and S.M. Kaber

Pade-Legendre Interpolants for Gibbs Reconstruction

J.S. Hesthaven, S.M. Kaber, and L. Lurati

A Survey of Parallel Mesh Generation Methods

N. Chrisochoides

High-Order Well-balanced Finite Volume WENO and Discontinuous Galerkin Methods for a Class of Hyperbolic Systems with Source Terms

Y. Xing and C.-W. Shu

An Adaptive Multi-Element Generalized Polynomial Chaos Method for Stochastic Differential Equations

X. Wan and G.E. Karniadakis

A Discontinuous Galerkin Method for Two-Temperature Plasmas

G. Lin and G.E. Karniadakis

Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation

X. Wan, D. Xiu, and G.E. Karniadakis

Adaptive Generalize Polynomial Chaos for Nonlinear Random Oscillations

D. Lucor and G.E. Karniadakis

The Interaction of a Shock and a Strong Vortex: Shock and Vortex Deformation and Vorticity and Sound Generation

S. Zhang, Y.-T. Zhang, and C.-W. Shu

A New Method to Impose No-Slip Boundary Conditions in Dissipative Particle Dynamics

I.V. Pivkin and G.E. Karniadakis

Equation-free/Galerkin-free POD-Assisted Computation of Incompressible Flows

S. Sirisup, D. Xiu, G.E. Karniadakis, and I.G. Kevrekidis

Error Estimates to Smooth Solutions of Runge-Kutta Discontinuous Galerkin Methods for Symmetrizable Systems of Conservation Laws

Q. Zhang and C.-W. Shu

High-Order Well-Balanced Finite Difference WENO Schemes for a Class of Hyperbolic Systems With Source Terms

Y. Xing and C.-W. Shu

Anti-Diffusive Flux Correction for High-Order Finite Difference WENO Schemes

Z. Xu and C.-W. Shu

Local Discontinuous Galerkin Methods for Two Classes of Two-Dimensional Nonlinear Wave Equations

Y. Xu and C.-W. Shu

The Stochastic Piston Problem

G. Lin, C.-H. Su, and G.E. Karniadakis

Hermite WENO Schemes For Hamilton-Jacobi Equations

J. Qiu and C.-W. Shu

A Comparison of Troubled Cell Indicators for Runge-Kutta Discontinuous Galerkin Methods Using WENO Limiters

J. Qiu and C.-W. Shu

Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

H. Atkins and C.-W. Shu

The Heterogeneous Multi-Scale Method Based on the Discontinuous Galerkin Method for Hyperbolic and Parabolic Problems

S. Chen, W.E., and C.-W. Shu

High Order Finite Difference WENO Schemes with the Exact Conservation Property for the Shallow Water Equations

Y. Xing and C.-W. Shu

Local Discontinuous Galerkin Methods for Nonlinear Shroedinger Equations

Y. Xu and C.-W. Shu

Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

D. Levy , S. Nayak, C.-W. Shu, and Y.-T. Zhang

Local Discontinuous Galerkin Methods for the Kuramoto-Sivashinsky Equations and the Ito-type Coupled KdV Equations

Y. Xu and C.-W. Shu

Analytical Theory of Grating Couplers for Waveguilde Sensing: A Perturbation Approach and its Limitations

R. Horvath, L.C. Wilcox, H.C. Pedersen, N. Skivesen, J.S. Hesthaven, and P.M. Johansen

A Hybrid Cosmological Hydrodynamic/N-Body Code Based on a Weighted Essentially Non-Oscillatory Scheme

L.-L. Feng, C.-W. Shu, and M. Zhang

Discontinuous Galerkin Methods for the Time-Domain Maxwell's Equations: An Introduction

J.S. Hesthaven and T. Warburton

Approximation of Hyperbolic Models for Chemosensitive Movements

F. Filbet and C.-W. Shu

Local Discontinuous Galerkin Methods for Three Classes of Nonlinear Wave Equations

Y. Xu and C.-W. Shu

The Discontinuous Galerkin Method with Lax-Wendroff Type Time Discretization

J. Qiu, M. Dumbser, and C.-W. Shu

Filtering in Legendre Spectral Methods

J.S. Hesthaven and R.M. Kirby

Uncertainly Analysis For Steady-State Inviscid Burgers' Equation

Q.Y. Chen, D. Gottlieb, and J.S. Hesthaven

Spectral Methods for Compressible Reactive Flows

D. Gottlieb and S. Gottlieb

Hermite WENO Schemes and Their Application As Limiters For Runge-Kutta Discontinuous Galerkin Method II: Two Dimensional Case

J. Qiu and C.-W. Shu

Reinterpretation and Simplified Implementation of a Discontinuous Galerkin Method for Hamilton-Jacobi Equations

F. Li and C.-W. Shu

A Spectral Multidomain Penalty Method Model For the Simulation of High Reynolds Number Localized Incompressible Stratified Turbulence

P.J. Diasmessis, J.A. Domaradzki, and J.S. Hesthaven

On the Computation of High-Order Pseudospectral Derivatives

B. Costa and W.S. Don

Spectral Convergence of Mapped Chebyshev Methods

B. Costa, W.S. Don, and A. Simas

Numerical Simulations of High Mach Number Astrophysical Jets With Radiative Cooling

Y. Ha, C.L. Gardner, A. Gelb, and C.-W. Shu

Local Divergence-Free Discontinuous Galerkin Methods for MHD Equations

F. Li and C.-W. Shu

Local Discontinuous Galerkin Methods for Nonlinear Dispersive Equations

D. Levy, C.-W. Shu, and J. Yan

Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs

Q.Y. Chen, D. Gottlieb, and J.S. Hesthaven

Simulation of Complex Viscoelastic Flows Using Fokker-Planck Equation: 3D FENE Model

C. Chauviere and A. Lozinski

Locally Divergence-Free Galerkin Methods for the Maxwell Equations

B. Cockburn, F. Li, and C.-W. Shu

Fourier-Pade Approximations and Filtering for the Spectral Simulations of Incompressible Boussinesq Convection Problem

M.S. Min, S.M Kaber, and W.S. Don

Hermite WENO Schemes and Their Application as Limiters for Runge-Kutta Discontinuous Galerkin Method: One Dimensional Case

J. Qiu and C.-W. Shu

Fast and Accurate Boundary Variation Method for Multi-Layered Diffractive Optics

L.C. Wilcox, P.G. Dinesen, and J.S. Hesthaven

High Order Nodal Discontinuous Galerkin Methods for the Maxwell Eigenvalue Problem

J.S. Hesthaven and T. Warburton

An Analysis Of and a Comparison Between the Discontinuous Galerkin and the Spectral Finite Volume Methods

M. Zhang and C.-W. Shu

On a One-Sided Post-Processing Technique for the Discontinuous Galerkin Methods

J. Ryan and C.-W. Shu

Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters

J. Qiu and C.-W. Shu

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

D. Xiu and G.E. Karniadakis

Modeling Uncertainty in Flow Simulations Via Generalized Polynomial Chaos

D. Xiu and G.E. Karniadakis

Modeling Uncertainty in Steady-State Diffusion Problems Via Generalized Polynomial Chaos

D. Xiu and G.E. Karniadakis

Domain Decomposition Spectral Approximations for an Eigenvalue Problem with a Piecewise Constant Coefficient

M.S. Min and D. Gottlieb

Extension of a Post-Porcessing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Applications to an Aeroacoustic Problem

J. Ryan, C.-W. Shu, and H. Atkins

Numerical Convergence Study of Nearly-Incompressible, Inviscid Taylor-Green Vortex Flow

W.S. Don, D. Gottlieb, C.-W. Shu, O. Shilling, L. Jameson

A Fast Solver for Fokker-Planck Equation Applied to Viscoelastic Flow Calculations

A. Lozinski and C. Chauviere

A Spectral Vanishing Viscosity Method for Stabilizing Low-Dimensional Galerkin Systems

S. Sirisup and G. E. Karniadakis

On the Constants in hp-Finite Element Trace Inequalities

T. Warburton and J. S. Hesthaven

A Fokker-Planck Simulation of Fast Flows of Concentrated Polymer Solutions in Complex Geometries

A. Lozinski, C. Chauviere, J. Fang, and R. G. Owens

High-Order Accurate Methods in Time-Domain Computational Electromagnetics: A Review

J. S. Hesthaven

Spatial Discretization Of the Dusty Gas Equations

D. Gottlieb and R. Teman

High-Order Accurate Methods For Time-Domain Electromagnetics

J.S. Hesthaven and T. Warburton

P-Refinement and P-Threads

S. Dong and G.E. Karniadakis

An Analysis of Three Different Formulations of the Discontinuous Galerkin Method For Diffusion Equations

M. Zhang and C.-W. Shu

Finite Difference WENO Schemes With Lax-Wendroff Type Time Discretizations

J. Qiu and C.-W. Shu

Multi-Domain WENO Finite Difference Method With Implementation at Sub-Domain Interfaces

K. Sebastian and C.-W. Shu

Simulation of Dilute Polymer Solutions Using a Fokker-Planck Equation

C. Chauviere and A. Lozinski

On the Engquist-Majda Absorbing Boundary Conditions for Hyperbolic Systems

A. Ditkowski and D. Gottlieb

Resolution of High-Order WENO Schemes for Complicated Flow Structures

J. Shi, Y. T. Zhang, and C.-W. Shu

A Weighted Essentially Non-Oscillatory Numerical Scheme for a Multi-Class LWR Model

M. Zhang, C.-W. Shu, G. C. K. Wong, and S. C. Wong

A Multi-Domain Spectral Method for Supersonic Reactive Flows

W.S. Don, D. Gottlieb, and J.H. Jung

Error Estimates to Smooth Solutions of Runge-Kutta Discontinuous Galerkin Methods For Scalar Conservation Laws

Q. Zhang and C.-W. Shu

On the Convergence of the Fourier Approximation For Eigenvalues and Eigenfunctions of Discontinuous Problems

M.S. Min and D. Gottlieb

A WENO-Solver For the Transients of Boltzmann-Poisson System for Semiconductor Devices. Performance and Comparisons With Monte-Carlo Methods

J. A. Carrillo, I. M. Gamba, A. Majorana, and C.-W. Shu

An Efficient Technique For Simulation of Viscoelastic Flows Derived From the Brownian Configuration Field Method

Q. Zhang, M. Zhang, G. Jin, D. Lin, and C.-W. Shu

Modeling Numerical Methods and Simulation For Particle-Fluid Two-Phase Flow Problems

Q. Zhang, M. Zhang, G. Jin, D. Lin, and C.-W. Shu

Shock Capturing, Level Sets, and PDE-Based Methods in Computer Vision and Image Processing: A Review of Osher's Contribution

R. I. Fedkiw, G. Sapiro, and C.-W. Shu

Local Discontinuous Galerkin Methods For Partial Differential Equations With Higher-Order Derivatives

J. Yan and C.-W. Shu

Under-Resolution and Diagnostics in Spectral Simulations of Complex-Geometry Flows

R. M. Kirby and G. E. Karniadakis

A Semi-Lagrangian Method For Turbulence Simulations Using Mixed Spectral Discretizations

J. Xu, D. Xiu, and G. E. Karniadakis

Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation

M. Jardak, C. H. Su, and G. E. Karniadakis

Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos

d. Xiu, D. Lucor, C. H. Su, and G. E. Karniadakis

High-Order Unstructured Grid Methods for Time-Domain Electromagnetics

J. S. Hesthaven and T. Warburton</