Optimal Strong-Stability-Preserving Runge–Kutta Time Discretizations for Discontinuous Galerkin Methods

Ethan J. Kubatko, Benjamin Yeager, David I. Ketcheson

Type: Article

Publication Date: 2013-10-28

Citations: 61

DOI: https://doi.org/10.1007/s10915-013-9796-7

View Publication

Download PDF

Locations

Journal of Scientific Computing - View
King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Optimal implicit strong stability preserving Runge–Kutta methods	2008	David I. Ketcheson Colin B. Macdonald Sigal Gottlieb
+	Optimal Strong-Stability-Preserving Time-Stepping Schemes with Fast Downwind Spatial Discretizations	2006	Sigal Gottlieb Steven J. Ruuth
+	Time Step Restrictions for Strong-Stability-Preserving Multistep Runge–Kutta Discontinuous Galerkin Methods	2021	Benjamin Yeager Ethan J. Kubatko Dylan Wood
+	Optimal Runge–Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems	2011	Thomas Toulorge Wim Desmet
+	Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge–Kutta time discretizations	2006	Ethan J. Kubatko Joannes J. Westerink Clint Dawson
+	Strong stability-preserving three-derivative Runge–Kutta methods	2023	Xueyu Qin Zhenhua Jiang Jian Yu Lintao Huang Chao Yan
+	Strong Stability Preserving Explicit Runge—Kutta Methods	2011
+	Strong Stability-Preserving (SSP) High-Order Time Discretization Methods	2009	Xinghui Zhong
+	Optimal Error Estimates of the Local Discontinuous Galerkin Method and High-order Time Discretization Scheme for the Swift–Hohenberg Equation	2022	Lingling Zhou Ruihan Guo
+	Optimal Runge-Kutta Stability Polynomials for Multidimensional High-Order Methods	2021	Siavash Hedayati Nasab Carlos A. Pereira Brian C. Vermeire
+	Strong Stability Preserving Second Derivative General Linear Methods Based on Taylor Series Conditions for Discontinuous Galerkin Discretizations	2023	Afsaneh Moradi Ali Abdi Gholamreza Hojjati
+	Stability and Error Estimates of Ultra-Weak Local Discontinuous Galerkin Method with Spectral Deferred Correction Time-Marching for PDEs with High Order Spatial Derivatives	2024	Lingling Zhou Wenjuan Guo
+ PDF Chat	On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations	2005	Sigal Gottlieb
+ PDF Chat	Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems	2019	Guosheng Fu Chi‐Wang Shu
+	Optimal error estimate of discontinuous Galerkin methods for advection-diffusion-reaction problems with low regularity	2022	Zhiqiang Cai Jing Yang
+	Non-linear evolution using optimal fourth-order strong-stability-preserving Runge–Kutta methods	2003	Raymond J. Spiteri Steven J. Ruuth
+	Discontinuous Galerkin Methods with Optimal $$L^2$$ Accuracy for One Dimensional Linear PDEs with High Order Spatial Derivatives	2018	Pei Fu Yingda Cheng Fengyan Li Yan Xu
+	Globally optimal Runge-Kutta methods	1973	Ralph Marvin Toms
+	Strong-stability-preserving 3-stage Hermite–Birkhoff time-discretization methods	2010	Truong Nguyen-Ba Huong Nguyen-Thu Thierry Giordano Rémi Vaillancourt
+ PDF Chat	Accurate monotonicity-preserving schemes with Runge-Kutta time stepping	1997	Suresh Alapati H. Huynth Suresh Alapati H. Huynth

Works That Cite This (43)

Action	Title	Year	Authors
+ PDF Chat	High order explicit local time stepping methods for hyperbolic conservation laws	2019	Thi‐Thao‐Phuong Hoang Lili Ju Wei Leng Zhu Wang
+	Time Step Restrictions for Strong-Stability-Preserving Multistep Runge–Kutta Discontinuous Galerkin Methods	2021	Benjamin Yeager Ethan J. Kubatko Dylan Wood
+ PDF Chat	Implicit and implicit-explicit strong stability preserving Runge–Kutta methods with high linear order	2017	Sidafa Conde Sigal Gottlieb Zachary J. Grant John N. Shadid
+	Strong Stability Preserving Explicit Peer Methods for Discontinuous Galerkin Discretizations	2017	Marcel Klinge Rüdiger Weiner
+	Multirate time-integration based on dynamic ODE partitioning through adaptively refined meshes for compressible fluid dynamics	2024	Daniel Doehring Michael Schlottke‐Lakemper Gregor J. Gassner Manuel Torrilhon
+ PDF Chat	Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method	2021	Ravneet Kaur S Shallu Sachin Kumar V. K. Kukreja
+ PDF Chat	An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction	2017	Florian Blachère Rodolphe Turpault
+	Two different temporal domain integration schemes combined with compact finite difference method to solve modified Burgers’ equation	2021	Ravneet Kaur S Shallu V. K. Kukreja N. Parumasur P. Singh
+	ExWave: A high performance discontinuous Galerkin solver for the acoustic wave equation	2019	S. Schoeder Wolfgang A. Wall Martin Kronbichler
+	Optimal Runge-Kutta Stability Polynomials for Multidimensional High-Order Methods	2021	Siavash Hedayati Nasab Carlos A. Pereira Brian C. Vermeire

Works Cited by This (26)

Action	Title	Year	Authors
+	Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations	2011	Sigal Gottlieb David I. Ketcheson Chi‐Wang Shu
+	Runge-Kutta discontinuous Galerkin methods for convection-dominated problems	2000	Bernardo Cockburn Chi‐Wang Shu
+	Numerical Methods for Ordinary Differential Equations	2016	J. C. Butcher
+	None	2003	Sigal Gottlieb Lee-Ad Gottlieb
+	Global optimization of explicit strong-stability-preserving Runge-Kutta methods	2005	Steven J. Ruuth
+	One step integration methods with maximum stability regions	1984	Ingemar Kinnmark William G. Gray
+	Stability of the method of lines	1992	S C Reddy Lloyd N. Trefethen
+	New stability theorems concerning one-step numerical methods for ordinary differential equations	1983	Robert Vichnevetsky
+	Largest disk of stability of explicit Runge-Kutta methods	1978	Rolf Jeltsch Olavi Nevanlinna
+	Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations	2010	Yulong Xing Xiangxiong Zhang Chi‐Wang Shu