Numerical methods for changing type systems. (23rd June 2018)

• Record Type: Journal Article
• Authors: Franz, Sebastian; Trostorff, Sascha; Waurick, Marcus
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 2(2019)
• Page Start: 1009
• Page End: 1038
• Publication Date: 2018-06-23
• Subjects: evolutionary equations -- changing type system -- discontinuous Galerkin -- space-time approach; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry007
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this paper we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to the solution theory already developed, we frame our numerical method in a discontinuous Galerkin approach in time with certain exponentially weighted spaces combined with a finite element method in space.