The Theoretical Accuracy of Runge-Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error. - Mark H. Carpenter; David I. Gottlieb; Saul Abarbanel; Wai-Sun Don (SIAM J. Sci. Comput., 1995)

On the Removal of Boundary Errors Caused by Runge-Kutta Integration of Nonlinear Partial Differential Equations. - Saul Abarbanel; David I. Gottlieb; Mark H. Carpenter (SIAM J. Sci. Comput., 1996)

Computational Considerations for the Simulation of Shock-Induced Sound. - Jay Casper; Mark H. Carpenter (SIAM J. Sci. Comput., 1998)

On the Conservation and Convergence to Weak Solutions of Global Schemes. - Mark H. Carpenter; David I. Gottlieb; Chi-Wang Shu (J. Sci. Comput., 2003)

Foreword. - Mark H. Carpenter; David I. Gottlieb; Jan S. Hesthaven; Chi-Wang Shu (J. Sci. Comput., 2005)

Fourth-Order Runge-Kutta Schemes for Fluid Mechanics Applications. - Mark H. Carpenter; C. A. Kennedy; Hester Bijl; S. A. Viken; Veer N. Vatsa (J. Sci. Comput., 2005)

Idempotent filtering in spectral and spectral element methods. - Alex Kanevsky; Mark H. Carpenter; Jan S. Hesthaven (J. Comput. Phys., 2006)

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. - Alex Kanevsky; Mark H. Carpenter; David I. Gottlieb; Jan S. Hesthaven (J. Comput. Phys., 2007)

A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions. - Magnus Svärd; Mark H. Carpenter; Jan Nordström (J. Comput. Phys., 2007)

Third-order Energy Stable WENO scheme. - Nail K. Yamaleev; Mark H. Carpenter (J. Comput. Phys., 2009)

A systematic methodology for constructing high-order energy stable WENO schemes. - Nail K. Yamaleev; Mark H. Carpenter (J. Comput. Phys., 2009)

Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators. - Mark H. Carpenter; Jan Nordström; David I. Gottlieb (J. Sci. Comput., 2010)

Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods. - Ken Mattsson; Mark H. Carpenter (SIAM J. Sci. Comput., 2010)

Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes. - Travis C. Fisher; Mark H. Carpenter; Nail K. Yamaleev; Steven H. Frankel (J. Comput. Phys., 2011)

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains. - Travis C. Fisher; Mark H. Carpenter (J. Comput. Phys., 2013)

Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions. - Travis C. Fisher; Mark H. Carpenter; Jan Nordström; Nail K. Yamaleev; Charles Swanson (J. Comput. Phys., 2013)

Optimal diagonal-norm SBP operators. - Ken Mattsson; Martin Almquist; Mark H. Carpenter (J. Comput. Phys., 2014)

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces. - Mark H. Carpenter; Travis C. Fisher; Eric J. Nielsen; Steven H. Frankel (SIAM J. Sci. Comput., 2014)

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations. - Matteo Parsani; Mark H. Carpenter; Eric J. Nielsen (J. Comput. Phys., 2015)

Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. - Matteo Parsani; Mark H. Carpenter; Eric J. Nielsen (J. Comput. Phys., 2015)

Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier-Stokes Equations. - Matteo Parsani; Mark H. Carpenter; Travis C. Fisher; Eric J. Nielsen (SIAM J. Sci. Comput., 2016)

Corrigendum to "A stable and conservative interface treatment of arbitrary spatial accuracy" [J. Comput. Phys. 148 (1999) 341-365]. - Mark H. Carpenter; Jan Nordström; David I. Gottlieb (J. Comput. Phys., 2017)

A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier-Stokes equations. - Nail K. Yamaleev; Mark H. Carpenter (J. Comput. Phys., 2017)

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements. - Jared Crean; Jason E. Hicken; David C. Del Rey Fernández; David W. Zingg; Mark H. Carpenter (J. Comput. Phys., 2018)

An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. - Lucas Friedrich; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Matteo Parsani; Mark H. Carpenter (J. Sci. Comput., 2018)

Entropy Stability and the No-Slip Wall Boundary Condition. - Magnus Svärd; Mark H. Carpenter; Matteo Parsani (SIAM J. Numer. Anal., 2018)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Euler equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; L. Fredrich; Diego Rojas; Andrew R. Winters; Gregor J. Gassner; Stefano Zampini; Matteo Parsani (CoRR, 2019)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; Lucas Friedrich; Andrew R. Winters; Gregor J. Gassner; Matteo Parsani (CoRR, 2019)

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier-Stokes Equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; Stefano Zampini; Matteo Parsani (CoRR, 2019)

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids. - Longfei Gao; David C. Del Rey Fernández; Mark H. Carpenter; David E. Keyes (J. Comput. Appl. Math., 2019)

Conservative and entropy stable solid wall boundary conditions for the compressible Navier-Stokes equations: Adiabatic wall and heat entropy transfer. - Lisandro Dalcín; Diego Rojas; Stefano Zampini; David C. Del Rey Fernández; Mark H. Carpenter; Matteo Parsani (J. Comput. Phys., 2019)

Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates. - David C. Del Rey Fernández; Jared Crean; Mark H. Carpenter; Jason E. Hicken (J. Comput. Phys., 2019)

Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids. - Nail K. Yamaleev; David C. Del Rey Fernández; Jialin Lou; Mark H. Carpenter (J. Comput. Phys., 2019)

Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates. - David C. Del Rey Fernández; Pieter D. Boom; Mark H. Carpenter; David W. Zingg (J. Sci. Comput., 2019)

Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. - Lucas Friedrich; Gero Schnücke; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Mark H. Carpenter (J. Sci. Comput., 2019)

Efficient Entropy Stable Gauss Collocation Methods. - Jesse Chan; David C. Del Rey Fernández; Mark H. Carpenter (SIAM J. Sci. Comput., 2019)

Accurate solution-adaptive finite difference schemes for coarse and fine grids. - Viktor Linders; Mark H. Carpenter; Jan Nordström (J. Comput. Phys., 2020)

Provably stable flux reconstruction high-order methods on curvilinear elements. - Alexander Cicchino; David C. Del Rey Fernández; Siva Nadarajah; Jesse Chan; Mark H. Carpenter (J. Comput. Phys., 2022)

Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy. - Michael Donello; Mark H. Carpenter; Hessam Babaee (SIAM J. Sci. Comput., 2022)

A superconvergent stencil-adaptive SBP-SAT finite difference scheme. - Viktor Linders; Mark H. Carpenter; Jan Nordström (J. Comput. Phys., 2024)