Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators
DOI10.1007/s42967-019-00057-2zbMath1476.65281arXiv1908.08732OpenAlexW3106538085MaRDI QIDQ2665571
Philip Heinisch, Hendrik Ranocha, Katharina Ostaszewski
Publication date: 19 November 2021
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.08732
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Finite difference methods for boundary value problems involving PDEs (65N06) Applications to the sciences (65Z05)
Related Items (3)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Optimal diagonal-norm SBP operators
- Review of summation-by-parts schemes for initial-boundary-value problems
- A generalized framework for nodal first derivative summation-by-parts operators
- Summation-by-parts operators and high-order quadrature
- A note on \(L^{\infty }\) bounds and convergence rates of summation-by-parts schemes
- Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
- Mimetic finite difference method
- On the order of accuracy for difference approximations of initial-boundary value problems
- Discrete Helmholtz-Hodge decomposition on polyhedral meshes using compatible discrete operators
- A primal formulation for the Helmholtz decomposition
- Lectures in magnetohydrodynamics. With an appendix on extended MHD
- Summation by parts for finite difference approximations for \(d/dx\)
- On coordinate transformations for summation-by-parts operators
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
- Compatible diagonal-norm staggered and upwind SBP operators
- Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
- Energy stable and high-order-accurate finite difference methods on staggered grids
- Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods
- On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma
- SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids
- Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
- Summation by parts operators for finite difference approximations of second derivatives
- Fast discrete Helmholtz-Hodge decompositions in bounded domains
- Turbulence in magnetohydrodynamics
- Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives
- Numerical generation of vector potentials from specified magnetic fields
- Some notes on summation by parts time integration methods
- Boundary optimized diagonal-norm SBP operators
- Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates
- Summation-by-parts operators for correction procedure via reconstruction
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Julia: A Fresh Approach to Numerical Computing
- LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
- LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property
- Finite Element Methods for Navier-Stokes Equations
- Magnetostatic and Electrostatic Problems in Inhomogeneous Anisotropic Media with Irregular Boundary and Mixed Boundary Conditions
- LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
- Vector potentials in three-dimensional non-smooth domains
- The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
- On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form
- Finite volume approximations and strict stability for hyperbolic problems
This page was built for publication: Discrete vector calculus and Helmholtz Hodge decomposition for classical finite difference summation by parts operators
