A new variational discretization technique for initial value problems bypassing governing equations

DOI10.1016/j.jcp.2023.111942OpenAlexW4317521188MaRDI QIDQ2683240

Alexander Rothkopf, Jan Nordström

Publication date: 10 February 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.14028

zbMATH Keywords

variational principleinitial value problemsummation by parts

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Related Items

A symmetry and Noether charge preserving discretization of initial value problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Summation-by-parts in time
• Review of summation-by-parts schemes for initial-boundary-value problems
• The SBP-SAT technique for initial value problems
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
• A roadmap to well posed and stable problems in computational physics
• On long time error bounds for the wave equation on second order form
• Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
• A new class of \(A\) stable summation by parts time integration schemes with strong initial conditions
• Convergence of energy stable finite-difference schemes with interfaces
• Properties of Runge-Kutta-summation-by-parts methods
• Analysis of the SBP-SAT stabilization for finite element methods. I: Linear problems
• On the convergence rates of energy-stable finite-difference schemes
• Uniformly best wavenumber approximations by spatial central difference operators
• Summation-by-parts operators for correction procedure via reconstruction
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
• Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems
• Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators
• Summation-By-Parts in Time: The Second Derivative
• A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
• Error Bounded Schemes for Time-dependent Hyperbolic Problems
• A Stable Penalty Method for the Compressible Navier–Stokes Equations: I. Open Boundary Conditions