A stable and dual consistent boundary treatment using finite differences on summation-by-parts form
2012 (English)In: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Conference paper (Other academic)
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.
Place, publisher, year, edition, pages
Vienna University of Technology , 2012.
Superconvergence, functionals, summation-by-parts, weak boundary conditions, stability, dual consistency
IdentifiersURN: urn:nbn:se:liu:diva-81890ISBN: 978-3-9503537-0-9OAI: oai:DiVA.org:liu-81890DiVA: diva2:556560
(ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 10-14, 2012