Entropy stabilization and property-preserving limiters for ℙ1 discontinuous Galerkin discretizations of scalar hyperbolic problems

Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points

(2020) Jan Glaubitz et al.   APPLIED NUMERICAL MATHEMATICS

Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws

(2020) Dmitri Kuzmin   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Locally bound-preserving enriched Galerkin methods for the linear advection equation

(2020) Dmitri Kuzmin et al.   COMPUTERS & FLUIDS

Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws

(2020) Dmitri Kuzmin et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws

(2020) Dmitri Kuzmin et al.   COMPUTERS & FLUIDS

A Moment Limiter for the Discontinuous Galerkin Method on Unstructured Triangular Meshes

(2019) Andrew Giuliani et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method

(2019) Will Pazner et al.   JOURNAL OF SCIENTIFIC COMPUTING

Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations

(2019) Hennes Hajduk et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes

(2018) R. Abgrall   JOURNAL OF COMPUTATIONAL PHYSICS

Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations

(2018) Yi Jiang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems

(2018) Jean-Luc Guermond et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

(2017) R. Anderson et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

(2017) Tianheng Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Invariant Domains and Second-Order Continuous Finite Element Approximation for Scalar Conservation Equations

(2017) Jean-Luc Guermond et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

(2016) Deep Ray et al.   Communications in Computational Physics

Positivity-Preserving Discontinuous Galerkin Methods with Lax–Wendroff Time Discretizations

(2016) Scott A. Moe et al.   JOURNAL OF SCIENTIFIC COMPUTING

Analysis of Algebraic Flux Correction Schemes

(2016) Gabriel R. Barrenechea et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems

(2016) Jean-Luc Guermond et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A maximum-principle preserving finite element method for scalar conservation equations

(2014) Jean-Luc Guermond et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

(2014) Jean-Luc Guermond et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces

(2014) Mark H. Carpenter et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

(2013) Travis C. Fisher et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Slope limiting for discontinuous Galerkin approximations with a possibly non-orthogonal Taylor basis

(2012) Dmitri Kuzmin   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments

(2011) X. Zhang et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

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

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2009) Dmitri Kuzmin   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws

(2008) Ivan Christov et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2008) Hong Luo et al.   JOURNAL OF COMPUTATIONAL PHYSICS