Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

doi:10.1016/j.jcp.2018.01.048

Title: Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Abstract

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of timemore »« less

Authors:

Mabuza, Sibusiso ^[1]; Shadid, John N. ^[2]; Kuzmin, Dmitri ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Mathematics and Statistics
Technical Univ. of Dortmund, Dortmund (Germany). Inst. of Applied Mathematics (LS III)

Publication Date:: Fri Feb 02 00:00:00 EST 2018

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1464187

Alternate Identifier(s):: OSTI ID: 1548780

Report Number(s):: SAND-2017-8659J
Journal ID: ISSN 0021-9991; 663067; TRN: US1902374

Grant/Contract Number:: AC04-94AL85000; NA0003525

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 361; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Local bounds preserving stabilization; Continuous Galerkin; Hyperbolic systems; Local extremum diminishing; Nodal variational stabilization

Citation Formats


                    Mabuza, Sibusiso, Shadid, John N., and Kuzmin, Dmitri. Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems.  United States: N. p., 2018. 
Web.  doi:10.1016/j.jcp.2018.01.048.

Copy to clipboard


                    Mabuza, Sibusiso, Shadid, John N., & Kuzmin, Dmitri. Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems.  United States.  https://doi.org/10.1016/j.jcp.2018.01.048

Copy to clipboard


                    Mabuza, Sibusiso, Shadid, John N., and Kuzmin, Dmitri. Fri .  
"Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems".  United States.  https://doi.org/10.1016/j.jcp.2018.01.048.  https://www.osti.gov/servlets/purl/1464187.

Copy to clipboard


                    
@article{osti_1464187,

  title        = {Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems},

  author       = {Mabuza, Sibusiso and Shadid, John N. and Kuzmin, Dmitri},

  abstractNote = {The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. In conclusion, for time discretization, Crank–Nicolson scheme and backward Euler scheme are utilized.},

  doi          = {10.1016/j.jcp.2018.01.048},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 361,

  place        = {United States},

  year         = {Fri Feb 02 00:00:00 EST 2018},

  month        = {Fri Feb 02 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.jcp.2018.01.048

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

Sod, Gary A.
Journal of Computational Physics, Vol. 27, Issue 1
DOI: 10.1016/0021-9991(78)90023-2

TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems
journal, September 1989

Cockburn, Bernardo; Lin, San-Yih; Shu, Chi-Wang
Journal of Computational Physics, Vol. 84, Issue 1
DOI: 10.1016/0021-9991(89)90183-6

Synchronized flux limiting for gas dynamics variables
journal, December 2016

Lohmann, Christoph; Kuzmin, Dmitri
Journal of Computational Physics, Vol. 326
DOI: 10.1016/j.jcp.2016.09.025

The group finite element formulation
journal, April 1983

Fletcher, C. A. J.
Computer Methods in Applied Mechanics and Engineering, Vol. 37, Issue 2
DOI: 10.1016/0045-7825(83)90122-6

A high-resolution finite element scheme for convection-dominated transport
journal, March 2000

Kuzmin, Dmitri
Communications in Numerical Methods in Engineering, Vol. 16, Issue 3
DOI: 10.1002/(SICI)1099-0887(200003)16:3<215::AID-CNM326>3.0.CO;2-1

Explicit and implicit FEM-FCT algorithms with flux linearization
journal, April 2009

Kuzmin, Dmitri
Journal of Computational Physics, Vol. 228, Issue 7
DOI: 10.1016/j.jcp.2008.12.011

Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations: Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations
journal, February 2017

Kuzmin, Dmitri; Shadid, John N.
International Journal for Numerical Methods in Fluids, Vol. 84, Issue 11
DOI: 10.1002/fld.4365

Failsafe flux limiting and constrained data projections for equations of gas dynamics
journal, November 2010

Kuzmin, Dmitri; Möller, Matthias; Shadid, John N.
Journal of Computational Physics, Vol. 229, Issue 23
DOI: 10.1016/j.jcp.2010.08.009

High-resolution FEM–FCT schemes for multidimensional conservation laws
journal, November 2004

Kuzmin, D.; Möller, M.; Turek, S.
Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 45-47
DOI: 10.1016/j.cma.2004.05.009

Linearity-preserving monotone local projection stabilization schemes for continuous finite elements
journal, August 2017

Kuzmin, Dmitri; Basting, Steffen; Shadid, John N.
Computer Methods in Applied Mechanics and Engineering, Vol. 322
DOI: 10.1016/j.cma.2017.04.030

Flux Correction Tools for Finite Elements
journal, January 2002

Kuzmin, D.; Turek, S.
Journal of Computational Physics, Vol. 175, Issue 2
DOI: 10.1006/jcph.2001.6955

A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics
journal, December 2010

Scovazzi, G.; Shadid, J. N.; Love, E.
Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 49-52
DOI: 10.1016/j.cma.2010.03.027

Stabilized shock hydrodynamics: I. A Lagrangian method
journal, January 2007

Scovazzi, G.; Christon, M. A.; Hughes, T. J. R.
Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6
DOI: 10.1016/j.cma.2006.08.008

Implicit total variation diminishing (TVD) schemes for steady-state calculations
journal, February 1985

Yee, H. C.; Warming, R. F.; Harten, A.
Journal of Computational Physics, Vol. 57, Issue 3
DOI: 10.1016/0021-9991(85)90183-4

New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws
journal, May 2008

Christov, Ivan; Popov, Bojan
Journal of Computational Physics, Vol. 227, Issue 11
DOI: 10.1016/j.jcp.2008.02.007

Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
journal, January 2016

Guermond, Jean-Luc; Popov, Bojan
SIAM Journal on Numerical Analysis, Vol. 54, Issue 4
DOI: 10.1137/16M1074291

Entropy–viscosity method for the single material Euler equations in Lagrangian frame
journal, March 2016

Guermond, Jean-Luc; Popov, Bojan; Tomov, Vladimir
Computer Methods in Applied Mechanics and Engineering, Vol. 300
DOI: 10.1016/j.cma.2015.11.009

Entropy viscosity method for nonlinear conservation laws
journal, May 2011

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan
Journal of Computational Physics, Vol. 230, Issue 11
DOI: 10.1016/j.jcp.2010.11.043

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG
journal, June 2016

Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.
Computer Methods in Applied Mechanics and Engineering, Vol. 304
DOI: 10.1016/j.cma.2016.01.019

A Newton-like finite element scheme for compressible gas flows
journal, July 2011

Gurris, Marcel; Kuzmin, Dmitri; Turek, Stefan
Computers & Fluids, Vol. 46, Issue 1
DOI: 10.1016/j.compfluid.2011.01.025

A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements
journal, July 2011

López Ortega, A.; Scovazzi, G.
Journal of Computational Physics, Vol. 230, Issue 17
DOI: 10.1016/j.jcp.2011.05.005

The numerical simulation of two-dimensional fluid flow with strong shocks
journal, April 1984

Woodward, Paul; Colella, Phillip
Journal of Computational Physics, Vol. 54, Issue 1
DOI: 10.1016/0021-9991(84)90142-6

Finite element flux-corrected transport (FEM-FCT) for the euler and Navier-Stokes equations
journal, October 1987

Löhner, Rainald; Morgan, Ken; Peraire, Jaime
International Journal for Numerical Methods in Fluids, Vol. 7, Issue 10
DOI: 10.1002/fld.1650071007

Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization
journal, January 2017

Badia, Santiago; Bonilla, Jesús
Computer Methods in Applied Mechanics and Engineering, Vol. 313
DOI: 10.1016/j.cma.2016.09.035

Strong Stability-Preserving High-Order Time Discretization Methods
journal, January 2001

Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan
SIAM Review, Vol. 43, Issue 1
DOI: 10.1137/S003614450036757X

High Order Strong Stability Preserving Time Discretizations
journal, September 2008

Gottlieb, Sigal; Ketcheson, David I.; Shu, Chi-Wang
Journal of Scientific Computing, Vol. 38, Issue 3
DOI: 10.1007/s10915-008-9239-z

A nonlinear ALE-FCT scheme for non-equilibrium reactive solute transport in moving domains
journal, September 2014

Mabuza, Sibusiso; Kuzmin, Dmitri
International Journal for Numerical Methods in Fluids, Vol. 76, Issue 11
DOI: 10.1002/fld.3961

Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach
journal, October 2012

Scovazzi, G.
Journal of Computational Physics, Vol. 231, Issue 24
DOI: 10.1016/j.jcp.2012.06.033

Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion
journal, December 2008

John, Volker; Schmeyer, Ellen
Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 3-4
DOI: 10.1016/j.cma.2008.08.016

The node-centred finite volume approach: Bridge between finite differences and finite elements
journal, January 1993

Selmin, V.
Computer Methods in Applied Mechanics and Engineering, Vol. 102, Issue 1
DOI: 10.1016/0045-7825(93)90143-L

Unified Construction of Finite Element and Finite Volume Discretizations for Compressible Flows
journal, January 1996

Selmin, V.; Formaggia, L.
International Journal for Numerical Methods in Engineering, Vol. 39, Issue 1
DOI: 10.1002/(SICI)1097-0207(19960115)39:1<1::AID-NME837>3.0.CO;2-G

A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian–Eulerian flow computations
journal, August 2014

Zeng, X.; Scovazzi, G.
Journal of Computational Physics, Vol. 270
DOI: 10.1016/j.jcp.2014.03.054

Works referencing / citing this record:

Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems
journal, September 2020

Bonilla, Jesús; Badia, Santiago
Journal of Computational Physics, Vol. 416
DOI: 10.1016/j.jcp.2020.109522

On differentiable local bounds preserving stabilization for Euler equations
text, January 2019

Badia, Santiago; Bonilla, Jesús; Mabuza, Sibusiso
arXiv
DOI: 10.48550/arxiv.1911.06792

Similar Records in DOE PAGES and OSTI.GOV collections:

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

Journal Article Mabuza, Sibusiso ; Shadid, John N. ; Cyr, Eric C. ; ... - Journal of Computational Physics

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and themore »« less
Cited by 10
https://doi.org/10.1016/j.jcp.2020.109390

Full Text Available
On differentiable local bounds preserving stabilization for Euler equations

Journal Article Badia, Santiago ; Bonilla, Jesús ; Mabuza, Sibusiso ; ... - Computer Methods in Applied Mechanics and Engineering

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. Themore »« less
https://doi.org/10.1016/j.cma.2020.113267

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

Journal Article Hajduk, Hennes ; Kuzmin, Dmitri ; Kolev, Tzanio ; ... - Computer Methods in Applied Mechanics and Engineering

In this work, we introduce a new residual distribution (RD) framework for the design of bound-preserving high-resolution finite element schemes. The continuous and discontinuous Galerkin discretizations of the linear advection equation are modified to construct local extremum diminishing (LED) approximations. To that end, we perform mass lumping and redistribute the element residuals in a manner which guarantees the LED property. The hierarchical correction procedure for high-order Bernstein finite element discretizations involves localization to subcells and definition of bound-preserving weights for subcell contributions. Using strong stability preserving (SSP) Runge–Kutta methods for time integration, we prove the validity of discrete maximum principlesmore »« less
Cited by 10
https://doi.org/10.1016/j.cma.2019.112658

Full Text Available
Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

Journal Article Pazner, Will - Computer Methods in Applied Mechanics and Engineering

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when usedmore »« less
https://doi.org/10.1016/j.cma.2021.113876

Full Text Available
Explicit and implicit multidimensional compact high-resolution shock-capturing methods: Formulation

Journal Article Yee, H C - Journal of Computational Physics

Two families of explicit and implicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth- and sixth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These higher-order compact schemes require the same grid stencil per spatial direction as their second-order noncompact cousins. Themore »« less
https://doi.org/10.1006/jcph.1996.5608

Similar Records

Title: Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Abstract

Citation Formats

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws journal, April 1978

TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems journal, September 1989

Synchronized flux limiting for gas dynamics variables journal, December 2016

The group finite element formulation journal, April 1983

A high-resolution finite element scheme for convection-dominated transport journal, March 2000

Explicit and implicit FEM-FCT algorithms with flux linearization journal, April 2009

Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations: Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations journal, February 2017

Failsafe flux limiting and constrained data projections for equations of gas dynamics journal, November 2010

High-resolution FEM–FCT schemes for multidimensional conservation laws journal, November 2004

Linearity-preserving monotone local projection stabilization schemes for continuous finite elements journal, August 2017

Flux Correction Tools for Finite Elements journal, January 2002

A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics journal, December 2010

Stabilized shock hydrodynamics: I. A Lagrangian method journal, January 2007

Implicit total variation diminishing (TVD) schemes for steady-state calculations journal, February 1985

New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws journal, May 2008

Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems journal, January 2016

Entropy–viscosity method for the single material Euler equations in Lagrangian frame journal, March 2016

Entropy viscosity method for nonlinear conservation laws journal, May 2011

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG journal, June 2016

A Newton-like finite element scheme for compressible gas flows journal, July 2011

A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements journal, July 2011

The numerical simulation of two-dimensional fluid flow with strong shocks journal, April 1984

Finite element flux-corrected transport (FEM-FCT) for the euler and Navier-Stokes equations journal, October 1987

Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization journal, January 2017

Strong Stability-Preserving High-Order Time Discretization Methods journal, January 2001

High Order Strong Stability Preserving Time Discretizations journal, September 2008

A nonlinear ALE-FCT scheme for non-equilibrium reactive solute transport in moving domains journal, September 2014

Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach journal, October 2012

Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion journal, December 2008

The node-centred finite volume approach: Bridge between finite differences and finite elements journal, January 1993

Unified Construction of Finite Element and Finite Volume Discretizations for Compressible Flows journal, January 1996

A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian–Eulerian flow computations journal, August 2014

Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems journal, September 2020

On differentiable local bounds preserving stabilization for Euler equations text, January 2019

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems
journal, September 1989

Synchronized flux limiting for gas dynamics variables
journal, December 2016

The group finite element formulation
journal, April 1983

A high-resolution finite element scheme for convection-dominated transport
journal, March 2000

Explicit and implicit FEM-FCT algorithms with flux linearization
journal, April 2009

Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations: Gradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations
journal, February 2017

Failsafe flux limiting and constrained data projections for equations of gas dynamics
journal, November 2010

High-resolution FEM–FCT schemes for multidimensional conservation laws
journal, November 2004

Linearity-preserving monotone local projection stabilization schemes for continuous finite elements
journal, August 2017

Flux Correction Tools for Finite Elements
journal, January 2002

A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics
journal, December 2010

Stabilized shock hydrodynamics: I. A Lagrangian method
journal, January 2007

Implicit total variation diminishing (TVD) schemes for steady-state calculations
journal, February 1985

New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws
journal, May 2008

Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
journal, January 2016

Entropy–viscosity method for the single material Euler equations in Lagrangian frame
journal, March 2016

Entropy viscosity method for nonlinear conservation laws
journal, May 2011

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG
journal, June 2016

A Newton-like finite element scheme for compressible gas flows
journal, July 2011

A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements
journal, July 2011

The numerical simulation of two-dimensional fluid flow with strong shocks
journal, April 1984

Finite element flux-corrected transport (FEM-FCT) for the euler and Navier-Stokes equations
journal, October 1987

Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization
journal, January 2017

Strong Stability-Preserving High-Order Time Discretization Methods
journal, January 2001

High Order Strong Stability Preserving Time Discretizations
journal, September 2008

A nonlinear ALE-FCT scheme for non-equilibrium reactive solute transport in moving domains
journal, September 2014

Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach
journal, October 2012

Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion
journal, December 2008

The node-centred finite volume approach: Bridge between finite differences and finite elements
journal, January 1993

Unified Construction of Finite Element and Finite Volume Discretizations for Compressible Flows
journal, January 1996

A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian–Eulerian flow computations
journal, August 2014

Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems
journal, September 2020

On differentiable local bounds preserving stabilization for Euler equations
text, January 2019