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 …

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 …

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

A generalized framework is presented that extends the classical theory of finite-difference
summation-by-parts (SBP) operators to include a wide range of operators, where the main …

We present a fourth order accurate finite difference method for the elastic wave equation in
second order formulation, where the fourth order accuracy holds in both space and time. The …

Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …

Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by
parts. The SBP operator definition includes a weight matrix that is used formally for discrete …

Block-to-block interface interpolation operators are constructed for several common high-
order finite difference discretizations. In contrast to conventional interpolation operators …

The objective of the present paper is to demonstrate the effectiveness of a spatial
discretization based on summation-by-parts operators with simultaneous approximation …

Many applications rely on solving time-dependent partial differential equations (PDEs) that
include second derivatives. Summation-by-parts (SBP) operators are crucial for developing …