Diagonally implicit Runge-Kutta schemes: discrete energy-balance laws and compactness properties

DOI10.1515/jnma-2022-0069arXiv2205.13032MaRDI QIDQ6087388

Publication date: 11 December 2023

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.13032

zbMATH Keywords

compactness energy stability diagonally implicit Runge-Kutta discrete energy law telescopic cancellation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical analysis (65-XX)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Formulation of thermoelastic dissipative material behavior using GENERIC
Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Compact families of piecewise constant functions in $L^p (0,T;B)$
Unconditional convergence of DIRK schemes applied to dissipative evolution equations
A splitting method for incompressible flows with variable density based on a pressure Poisson equation
Compact sets in the space $L^ p(0,T;B)$
Algebraic stability and error propagation in Runge-Kutta methods
Sur la B-stabilité des méthodes de Runge-Kutta
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
$L_2$ stability of explicit Runge-Kutta schemes
Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations
Compactness of discrete approximate solutions to parabolic PDEs -- application to a turbulence model
A note on Aubin-Lions-Dubinskiĭ lemmas
Hybrid methods for radiation transport using diagonally implicit Runge-Kutta and space-time discontinuous Galerkin time integration
Structure preserving approximation of dissipative evolution problems
An energy stable Runge-Kutta method for convex gradient problems
Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations
A posteriori error analysis for higher order dissipative methods for evolution problems
Monotonicity for Runge-Kutta methods: inner product norms
Time Compactness Tools for Discretized Evolution Equations and Applications to Degenerate Parabolic PDEs
G-stability is equivalent toA-stability
Compactness Properties of the DG and CG Time Stepping Schemes for Parabolic Equations
Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density
Solving Ordinary Differential Equations I
Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems
Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
Stability Properties of Implicit Runge–Kutta Methods
Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
Non-linear stability of a general class of differential equation methods
A priori bounds for positive solutions of nonlinear elliptic equations
A stability property of implicit Runge-Kutta methods
Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
Stability Criteria for Implicit Runge–Kutta Methods
Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method
Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
Combined DG--CG Time Stepping for Wave Equations
Galerkin Finite Element Methods for Parabolic Problems
A-Stable Methods and Padé Approximations to the Exponential
A special stability problem for linear multistep methods
Equilibrated flux a posteriori error estimates in $L^2(H^1)$-norms for high-order discretizations of parabolic problems
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
Single and double generator bracket formulations of multicomponent fluids with irreversible processes
Nonlinear partial differential equations with applications
Numerical Methods for Ordinary Differential Equations

This page was built for publication: Diagonally implicit Runge-Kutta schemes: discrete energy-balance laws and compactness properties