Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …

Many evolution problems in physics are described by partial differential equations on an
infinite domain; therefore, one is interested in the solutions to such problems for a given …

High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

Time dependent problems frequently pose challenges in areas of science and engineering
dealing with numerical analysis, scientific computation, mathematical models, and most …

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

Nonlinear entropy stability is used to derive provably stable high-order finite difference
operators including boundary closure stencils, for the compressible Navier–Stokes …

Coherent features of a turbulent Mach 0.9, Reynolds number jet are educed from a high-
fidelity large eddy simulation. Besides the well-known Kelvin–Helmholtz instabilities of the …

Response modes computed via linear resolvent analysis of a turbulent mean-flow field have
been shown to qualitatively capture characteristics of the observed turbulent coherent …

Many books have been written on? nite difference methods (FDM), but there are good
reasons to write still another one. The main reason is that even if higher order methods have …