We study a higher derivative extension to General Relativity and present a fully nonlinear/
nonperturbative treatment to construct initial data and study its dynamical behavior in …

High-order accurate first derivative finite difference operators are derived that naturally
introduce artificial dissipation. The boundary closures are based on the diagonal-norm …

Summation-by-parts (SBP) operators are popular building blocks for systematically
developing stable and high-order accurate numerical methods for time-dependent …

We develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …

We consider constant-coefficient initial-boundary value problems, with a first or second
derivative in time and a highest spatial derivative of order q, and their semi-discrete finite …

Strictly stable high-order accurate finite difference approximations are derived, for linear
initial boundary value problems. The boundary closures are based on the diagonal-norm …

The main motivation with the present study is to achieve a provably stable high-order
accurate finite difference discretisation of linear first-order hyperbolic problems on a …

We introduce an energy stable, high-order-accurate finite difference approximation of the
dynamic, pure bending Kirchhoff plate equations for complex geometries and spatially …

We consider energy stable summation by parts finite difference methods (SBP-FD) for the
homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the …

We develop a numerical method for solving the acoustic wave equation in covariant form on
staggered curvilinear grids in an energy conserving manner. The use of a covariant basis …