@inproceedings{b49eb166d5b74398a6c0d07a60e32a4e,
title = "A stable and dual consistent boundary treatment using finite differences on summation-by-parts form",
abstract = "This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.",
keywords = "Dual consistency, Functionals, Stability, Summation-by-parts, Superconvergence, Weak boundary conditions",
author = "Jens Berg and Jan Nordstr{\"o}m",
year = "2012",
language = "English",
isbn = "9783950353709",
series = "ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers",
pages = "7557--7570",
booktitle = "ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers",
note = "6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 ; Conference date: 10-09-2012 Through 14-09-2012",
}