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Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

https://doi.org/10.1063/5.0066008

Finkelstein, Joshua ; Cheng, Chungho ; Fiorin, Giacomo ; Seibold, Benjamin ; Grønbech-Jensen, Niels ( November 2021 , The Journal of Chemical Physics)

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High-order finite element methods for a pressure Poisson equation reformulation of the Navier–Stokes equations with electric boundary conditions

https://doi.org/10.1016/j.cma.2020.113451

Rosales, Rodolfo Ruben ; Seibold, Benjamin ; Shirokoff, David ; Zhou, Dong ( January 2021 , Computer Methods in Applied Mechanics and Engineering)

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DIRK Schemes with High Weak Stage Order

https://doi.org/10.1007/978-3-030-39647-3_36

Ketcheson, D. ; Seibold, B. ; Shirokoff, D. ; Zhou, D. ( August 2020 , Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering. Springer.)
Sherwin, S. ; Moxey, D. ; Peiro, J. ; Vincent, P. ; Schwab, C. (Ed.)
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

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