The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems

Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

Journal of Scientific Computing

Numerical Comparison of WENO Finite Volume and Runge–Kutta Discontinuous Galerkin Methods

Journal of Scientific Computing

Flux correction tools for finite elements

Journal of Computational Physics

Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems

Mathematics of Computation

Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Journal of Computational Physics

hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization

Journal of Scientific Computing

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

Journal of Scientific Computing

ADER: Arbitrary High Order Godunov Approach

Journal of Scientific Computing

AMR vs High Order Schemes

Journal of Scientific Computing

Eigensolution analysis of the discontinuous Galerkin method with nonuniform grids: I. one space dimension

Journal of Computational Physics

Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation

Journal of Computational Physics

Resolution of high order WENO schemes for complicated flow structures

Journal of Computational Physics

Hyperbolic conservation laws with space-dependent flux: I. Characteristics theory and Riemann problem

Journal of Computational and Applied Mathematics

Finite element level set formulations for modelling multiphase flows

ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering

Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case

Journal of Computational Physics

High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations

Journal of Computational Physics

A sequence of absorbing boundary conditions for Maxwell's equations

Journal of Computational Physics

Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations

Journal of Scientific Computing

Local discontinuous Galerkin methods for nonlinear dispersive equations

Journal of Computational Physics

Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

Journal of Computational Physics

Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems

Journal of Computational Physics

High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter

Journal of Computational Physics

Towards an Efficient and Scalable Discontinuous Galerkin Atmospheric Model

IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14

Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension

Journal of Scientific Computing

Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations

Journal of Scientific Computing

L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems

Journal of Scientific Computing

High-order RKDG Methods for Computational Electromagnetics

Journal of Scientific Computing

Pseudospectral solution of linear evolution equations of second order in space and time on unstructured quadrilateral subdomain topologies

Journal of Computational Physics

High Performance Computing of Compressible Flows

HPCASIA '05 Proceedings of the Eighth International Conference on High-Performance Computing in Asia-Pacific Region

Flooding and drying in discontinuous Galerkin finite-element discretizations of shallow-water equations: part 1: One dimension

Journal of Scientific Computing

High-order RKDG methods for computational electromagnetics

Journal of Scientific Computing

Locally divergence-free discontinuous Galerkin methods for MHD equations

Journal of Scientific Computing

L2(H1) norm a posteriori error estimation for discontinuous Galerkin approximations of reactive transport problems

Journal of Scientific Computing

Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes

Journal of Scientific Computing

Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws

Journal of Scientific Computing

Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws

Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ

A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows

Journal of Computational Physics

Spectral difference method for unstructured grids I: basic formulation

Journal of Computational Physics

Discontinuous Galerkin method based on non-polynomial approximation spaces

Journal of Computational Physics

On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection

Journal of Computational Physics

Runge-Kutta discontinuous Galerkin methods for compressible two-medium flow simulations: One-dimensional case

Journal of Computational Physics

CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation

Journal of Computational Physics

Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations

Journal of Scientific Computing

A Numerical Comparison of the Lax-Wendroff Discontinuous Galerkin Method Based on Different Numerical Fluxes

Journal of Scientific Computing

A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations

Journal of Computational Physics

Solutions of Multi-dimensional Hyperbolic Systems of Conservation Laws by Square Entropy Condition Satisfying Discontinuous Galerkin Method

Journal of Scientific Computing

Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results

Applied Numerical Mathematics

A Runge-Kutta discontinuous Galerkin method for viscous flow equations

Journal of Computational Physics

Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations

Journal of Scientific Computing

A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids

Journal of Computational Physics

A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations

Journal of Computational Physics

Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations

Journal of Computational Physics

Local discontinuous Galerkin methods for the Cahn-Hilliard type equations

Journal of Computational Physics

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

Journal of Computational Physics

Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation

Journal of Computational Physics

Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes

Journal of Computational Physics

Shallow water model on cubed-sphere by multi-moment finite volume method

Journal of Computational Physics

A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

Journal of Computational Physics

A DGBGK scheme based on WENO limiters for viscous and inviscid flows

Journal of Computational Physics

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Journal of Computational Physics

A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes

Journal of Computational Physics

Discontinuous Hamiltonian Finite Element Method for Linear Hyperbolic Systems

Journal of Scientific Computing

A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids

Journal of Computational Physics

Superconvergence and time evolution of discontinuous Galerkin finite element solutions

Journal of Computational Physics

An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations

Journal of Computational Physics

A class of residual distribution schemes and their relation to relaxation systems

Journal of Computational Physics

Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids

Journal of Computational Physics

On the Stability and Accuracy of the Spectral Difference Method

Journal of Scientific Computing

Short Note: A stability analysis for the spectral volume method on tetrahedral grids

Journal of Computational Physics

One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields

Journal of Scientific Computing

Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method

Journal of Scientific Computing

Polymorphic nodal elements and their application in discontinuous Galerkin methods

Journal of Computational Physics

Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells

Journal of Computational Physics

Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics

Journal of Computational Physics

Spectral difference method for compressible flow on unstructured grids with mixed elements

Journal of Computational Physics

FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

Journal of Computational Physics

High order multi-moment constrained finite volume method. Part I: Basic formulation

Journal of Computational Physics

Hermite WENO Schemes and Their Application as Limiters for Runge-Kutta Discontinuous Galerkin Method, III: Unstructured Meshes

Journal of Scientific Computing

High-order accurate simulation of low-Mach laminar flow past two side-by-side cylinders using spectral difference method

Computers and Structures

Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations

Computers and Structures

Application of Discontinuous Galerkin Methods for Reaction-Diffusion Systems in Developmental Biology

Journal of Scientific Computing

Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs

Journal of Scientific Computing

Hierarchical reconstruction for spectral volume method on unstructured grids

Journal of Computational Physics

Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations

Journal of Computational Physics

A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids

Journal of Computational Physics

Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case

Journal of Computational Physics

Very-high-order weno schemes

Journal of Computational Physics

Local derivative post-processing for the discontinuous Galerkin method

Journal of Computational Physics

Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws

Applied Numerical Mathematics

Local Discontinuous Galerkin Finite Element Method and Error Estimates for One Class of Sobolev Equation

Journal of Scientific Computing

Finite element form of FDV for widely varying flowfields

Journal of Computational Physics

Local discontinuous Galerkin methods for the generalized Zakharov system

Journal of Computational Physics

Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation

Journal of Computational Physics

A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid

Journal of Computational Physics

A robust high-order residual distribution type scheme for steady Euler equations on unstructured grids

Journal of Computational Physics

On Source Terms and Boundary Conditions Using Arbitrary High Order Discontinuous Galerkin Schemes

International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems

A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods

Journal of Computational and Applied Mathematics

Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case

Journal of Computational Physics

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

Journal of Computational Physics

Nonuniform time-step Runge-Kutta discontinuous Galerkin method for Computational Aeroacoustics

Journal of Computational Physics

A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

Journal of Computational Physics

Hybrid weighted essentially non-oscillatory schemes with different indicators

Journal of Computational Physics

A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations

Journal of Scientific Computing

Quantification of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) Fields

Journal of Scientific Computing

A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy

Journal of Scientific Computing

An efficient local time-stepping scheme for solution of nonlinear conservation laws

Journal of Computational Physics

Absorbing boundary conditions for the Euler and Navier-Stokes equations with the spectral difference method

Journal of Computational Physics

An interface treating technique for compressible multi-medium flow with Runge-Kutta discontinuous Galerkin method

Journal of Computational Physics

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

Journal of Computational Physics

A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations

Journal of Computational Physics

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

Journal of Computational Physics

A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator

Journal of Computational Physics

A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator

Journal of Computational Physics

RKDG methods with WENO type limiters and conservative interfacial procedure for one-dimensional compressible multi-medium flow simulations

Applied Numerical Mathematics

A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions

Journal of Computational Physics

A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations

Journal of Computational Physics

Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension

SIAM Journal on Numerical Analysis

Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

SIAM Journal on Numerical Analysis

Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations

Journal of Computational Physics

A high-order finite volume method for systems of conservation laws-Multi-dimensional Optimal Order Detection (MOOD)

Journal of Computational Physics

Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations

Journal of Scientific Computing

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

Journal of Computational Physics

A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations

Journal of Computational Physics

A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems

Journal of Scientific Computing

Modelling variable density flow problems in heterogeneous porous media using the method of lines and advanced spatial discretization methods

Mathematics and Computers in Simulation

A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems

Journal of Scientific Computing

Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov-Poisson system

Journal of Computational Physics

Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

Journal of Computational Physics

Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions

SIAM Journal on Scientific Computing

A stable interface element scheme for the p-adaptive lifting collocation penalty formulation

Journal of Computational Physics

Positivity-preserving high order finite difference WENO schemes for compressible Euler equations

Journal of Computational Physics

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Journal of Computational Physics

Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

Journal of Computational Physics

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes

Journal of Scientific Computing

Well-conditioned Orthonormal Hierarchical $\mathcal{L}_{2}$ Bases on Rn Simplicial Elements

Journal of Scientific Computing

Runge-Kutta discontinuous Galerkin method for the approximation of Baer and Nunziato type multiphase models

Journal of Computational Physics

Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes

Journal of Scientific Computing

A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation

Journal of Scientific Computing

An Efficient Correction Method to Obtain a Formally Third-Order Accurate Flow Solver for Node-Centered Unstructured Grids

Journal of Scientific Computing

Mathematical models and methods in the water industry

Mathematical and Computer Modelling: An International Journal

A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids

Journal of Computational Physics

Efficient Implementation of Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions

Journal of Scientific Computing

Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations

SIAM Journal on Numerical Analysis

Alternating Evolution Schemes for Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing

A two-dimensional HLLC Riemann solver for conservation laws: Application to Euler and magnetohydrodynamic flows

Journal of Computational Physics

Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics

Journal of Computational Physics

A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system

Computers & Mathematics with Applications

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

Journal of Scientific Computing

A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations

Journal of Computational Physics

A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods

Journal of Computational Physics

A p-adaptive LCP formulation for the compressible Navier-Stokes equations

Journal of Computational Physics

Discontinuous Galerkin method for Navier-Stokes equations using kinetic flux vector splitting

Journal of Computational Physics

Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation

Journal of Computational Physics

Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes - Speed comparisons with Runge-Kutta methods

Journal of Computational Physics

WENO Schemes and Their Application as Limiters for RKDG Methods Based on Trigonometric Approximation Spaces

Journal of Scientific Computing

Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods

Numerical Algorithms

A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: Energy conservation and boundary effect

Journal of Computational Physics

Runge-Kutta discontinuous Galerkin methods with WENO limiter for the special relativistic hydrodynamics

Journal of Computational Physics

GPU accelerated discontinuous Galerkin methods for Euler equations and its adjoint

Proceedings of the High Performance Computing Symposium

Study of conservation and recurrence of Runge---Kutta discontinuous Galerkin schemes for Vlasov---Poisson systems

Journal of Scientific Computing

Discontinuous Galerkin method for Krause's consensus models and pressureless Euler equations

Journal of Computational Physics

A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems

Journal of Computational Physics

Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation

Journal of Computational and Applied Mathematics

An efficient correction procedure via reconstruction for simulation of viscous flow on moving and deforming domains

Journal of Computational Physics

An efficient parallel implementation of explicit multirate Runge-Kutta schemes for discontinuous Galerkin computations

Journal of Computational Physics

A High-Order Moving Mesh Kinetic Scheme Based on WENO Reconstruction for Compressible Flows on Unstructured Meshes

Journal of Scientific Computing

A Superconvergent Discontinuous Galerkin Method for Hyperbolic Problems on Tetrahedral Meshes

Journal of Scientific Computing

An h-adaptive RKDG method with troubled-cell indicator for two-dimensional hyperbolic conservation laws

Advances in Computational Mathematics

High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model

Journal of Computational Physics

Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium

Journal of Computational Physics

Hierarchical slope limiting in explicit and implicit discontinuous Galerkin methods

Journal of Computational Physics

Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations

Journal of Computational Physics

On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods

Journal of Computational Physics

An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements

Journal of Computational Physics

A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

Journal of Computational Physics

Multidimensional HLLC Riemann solver for unstructured meshes - With application to Euler and MHD flows

Journal of Computational Physics

Visualization of large-scale structures in spatially developing compressible mixing layers

Journal of Visualization

Visualization of compressibility effects on large-scale structures in compressible mixing layers

Journal of Visualization

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

Journal of Scientific Computing

An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system

Journal of Computational Physics