Total-variation-diminishing time discretizations

Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

Journal of Scientific Computing

Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation

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

Two Barriers on Strong-Stability-Preserving Time Discretization Methods

Journal of Scientific Computing

Strong Stability Preserving Properties of Runge–Kutta Time Discretization Methods for Linear Constant Coefficient Operators

Journal of Scientific Computing

Spectral (finite) volume method for conservation laws on unstructured grids: II. Extension to two-dimensional scalar equation

Journal of Computational Physics

Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods

Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II

Implicit-explicit time stepping with spatial discontinuous finite elements

Applied Numerical Mathematics

A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles

Journal of Computational Physics

Nessyahu--Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids

Applied Numerical Mathematics

An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface

Journal of Scientific Computing

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids III: One Dimensional Systems and Partition Optimization

Journal of Scientific Computing

On Strong Stability Preserving Time Discretization Methods

Journal of Scientific Computing

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

Journal of Computational Physics

High-order schemes for Hamilton-Jacobi equations on triangular meshes

Journal of Computational and Applied Mathematics

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

Journal of Computational Physics

A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit

Journal of Computational Physics

Implicit subgrid-scale modeling by adaptive deconvolution

Journal of Computational Physics

Finite-volume WENO schemes for three-dimensional conservation laws

Journal of Computational Physics

A Eulerian level set/vortex sheet method for two-phase interface dynamics

Journal of Computational Physics

ADER schemes for three-dimensional non-linear hyperbolic systems

Journal of Computational Physics

ADER schemes on adaptive triangular meshes for scalar conservation laws

Journal of Computational Physics

High-order linear multistep methods with general monotonicity and boundedness properties

Journal of Computational Physics

TVD Fluxes for the High-Order ADER Schemes

Journal of Scientific Computing

On High Order Strong Stability Preserving Runge---Kutta and Multi Step Time Discretizations

Journal of Scientific Computing

Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

Journal of Scientific Computing

Derivative Riemann solvers for systems of conservation laws and ADER methods

Journal of Computational Physics

Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems

Journal of Computational Physics

A level-set method for interfacial flows with surfactant

Journal of Computational Physics

Extension of the spectral volume method to high-order boundary representation

Journal of Computational Physics

Optimal Strong-Stability-Preserving Time-Stepping Schemes with Fast Downwind Spatial Discretizations

Journal of Scientific Computing

An adaptive local deconvolution method for implicit LES

Journal of Computational Physics

Spectral (finite) volume method for conservation laws on unstructured grids VI: Extension to viscous flow

Journal of Computational Physics

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

Journal of Computational Physics

A numerical scheme for ionizing shock waves

Journal of Computational Physics

Spectral difference method for unstructured grids I: basic formulation

Journal of Computational Physics

Stepsize restrictions for total-variation-boundedness in general Runge-Kutta procedures

Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)

Direct-expansion forms of ADER schemes for conservation laws and their verification

Journal of Computational Physics

Maintaining the point correspondence in the level set framework

Journal of Computational Physics

WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations

Journal of Computational and Applied Mathematics

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

Journal of Computational Physics

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

Journal of Scientific Computing

Geometric curve flows on parametric manifolds

Journal of Computational Physics

δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media

Applied Numerical Mathematics

A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions

Journal of Scientific Computing

Implicit--explicit methods based on strong stability preserving multistep time discretizations

Applied Numerical Mathematics

Finite element/volume solution to axisymmetric conservation laws

Journal of Computational Physics

Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm

Journal of Computational Physics

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

Journal of Scientific Computing

IMEX extensions of linear multistep methods with general monotonicity and boundedness properties

Journal of Computational Physics

Short Note: On the connection between the spectral volume and the spectral difference method

Journal of Computational Physics

A simple embedding method for solving partial differential equations on surfaces

Journal of Computational Physics

A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids

Journal of Computational Physics

On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes

Journal of Computational Physics

Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration

Journal of Computational Physics

A Numerical Study of Diagonally Split Runge---Kutta Methods for PDEs with Discontinuities

Journal of Scientific Computing

Strong stability of singly-diagonally-implicit Runge--Kutta methods

Applied Numerical Mathematics

On the Stability and Accuracy of the Spectral Difference Method

Journal of Scientific Computing

Discretization methods with analytical solutions for a convection-reaction equation with higher-order discretizations

International Journal of Computer Mathematics

Optimal implicit strong stability preserving Runge--Kutta methods

Applied Numerical Mathematics

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

Journal of Computational Physics

Multirate Explicit Adams Methods for Time Integration of Conservation Laws

Journal of Scientific Computing

High Order Strong Stability Preserving Time Discretizations

Journal of Scientific Computing

A central conservative scheme for general rectangular grids

Journal of Computational Physics

A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids

Numerical Analysis and Its Applications

Third-order Energy Stable WENO scheme

Journal of Computational Physics

Strong stability preserving hybrid methods

Applied Numerical Mathematics

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

Journal of Computational Physics

High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems

Journal of Scientific Computing

Characterizing Strong Stability Preserving Additive Runge-Kutta Methods

Journal of Scientific Computing

A systematic methodology for constructing high-order energy stable WENO schemes

Journal of Computational Physics

A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty

Journal of Scientific Computing

Stepsize restrictions for total-variation-boundedness in general Runge--Kutta procedures

Applied Numerical Mathematics

A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver

Journal of Scientific Computing

Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids

Journal of Computational Physics

On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics

Journal of Computational Physics

A new TVD-MUSCL scheme for hyperbolic conservation laws

Computers & Mathematics with Applications

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

Journal of Computational Physics

A numerical scheme for ionizing shock waves

Journal of Computational Physics

On maximum-principle-satisfying high order schemes for scalar conservation laws

Journal of Computational Physics

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Journal of Computational Physics

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

Journal of Computational Physics

A conservative immersed interface method for Large-Eddy Simulation of incompressible flows

Journal of Computational Physics

An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

Journal of Computational and Applied Mathematics

A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations

Journal of Scientific Computing

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

Journal of Computational Physics

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

Journal of Computational Physics

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Applied Numerical Mathematics

Optimal Explicit Strong-Stability-Preserving General Linear Methods

SIAM Journal on Scientific Computing

Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation

Journal of Computational Physics

On the Linear Stability of the Fifth-Order WENO Discretization

Journal of Scientific Computing

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

Journal of Computational Physics

Step Sizes for Strong Stability Preservation with Downwind-Biased Operators

SIAM Journal on Numerical Analysis

Solving the euler equations on graphics processing units

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV

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

Strong-Stability-Preserving 7-Stage Hermite---Birkhoff Time-Discretization Methods

Journal of Scientific Computing

Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

Journal of Scientific Computing

Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics

Journal of Computational Physics

Shallow water simulations on multiple GPUs

PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2

Total variation diminishing nonstandard finite difference schemes for conservation laws

Mathematical and Computer Modelling: An International Journal

Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations

SIAM Journal on Scientific Computing

A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids

SIAM Journal on Scientific Computing

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

SIAM Journal on Scientific Computing

Discontinuous Galerkin Approximation of Relaxation Models for Linear and Nonlinear Diffusion Equations

SIAM Journal on Scientific Computing

Strong Stability Preserving Two-step Runge-Kutta Methods

SIAM Journal on Numerical Analysis

The existence of stepsize-coefficients for boundedness of linear multistep methods

Applied Numerical Mathematics

Simulations of Supersonic Astrophysical Jets and Their Environments Using Level Set Methods

Journal of Scientific Computing

Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities

Journal of Computational Physics

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

Journal of Computational Physics

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

Journal of Computational Physics

Strong Stability for Runge---Kutta Schemes on a Class of Nonlinear Problems

Journal of Scientific Computing

Short note: An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes

Journal of Computational Physics

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

Journal of Computational Physics

A level-set method for two-phase flows with moving contact line and insoluble surfactant

Journal of Computational Physics