Initial-Boundary Value Problems and the Navier-Stokes Equations

By H. Kreiss, J. Lorenz. 2004

630 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/d155b94dec851fc5618776330f0de58637623373

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In Computational Mechanics

In Mechanics of Materials

In Ocean Engineering

Citations in the corpus

Review of summation-by-parts schemes for initial-boundary-value problems (2013, methodology): “This approach is justiﬁable, at least if the energy method is used to prove stability, see [KL89, MS10].”
On the long-time behavior of unsplit perfectly matched layers (2004, background): “Proof: This is a consequence of the fact that (14) is a zero-order perturbation of a symmetric hyperbolic system (thus, strongly well posed) (see [19]).”
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (2014, methodology): “Nevertheless, for certain classes of PDEs, which the Euler and NS equations belong to, and with some restrictions on the solution, it can be shown that the constant-coefficient analysis is sufficient [76].”
Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I (2005, methodology): “Then, following standard ideas of Fourier analysis for linear constant coefficient problems (e.g. Kreiss and Lorenz, 1989), it suffices to consider initial data for (29) of the type ( ) ( )ˆ,0 i xr x e rω ω= , (30) where isω is an arbitrarily fixed wavenumber for perturbations, and r̂ is a bounded…”
A review of numerical methods for nonlinear partial differential equations (2012, neutral): “The compressible Navier–Stokes equations [56, 140] provide a macroscopic description of gases; the incompressible Navier–Stokes equations [51, 139, 144, 124] govern a macroscopic dynamics of liquids.”
Stability of perfectly matched layers, group velocities and anisotropic waves (2003, neutral): “Let us briefly recall the definitions of hyperbolicity (see [26]).”
Numerical Methods for Evolutionary Differential Equations (2008, background): “The book by Kreiss and Lorenz [111] covers well-posedness in depth.”