A stable and dual consistent boundary treatment using finite differences on summation-by-parts form

Jens Berg, Jan Nordström

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages7557-7570
Number of pages14
Publication statusPublished - 2012
Externally publishedYes
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: 10 Sept 201214 Sept 2012

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Conference

Conference6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Country/TerritoryAustria
CityVienna
Period10/09/1214/09/12

Keywords

  • Dual consistency
  • Functionals
  • Stability
  • Summation-by-parts
  • Superconvergence
  • Weak boundary conditions

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

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