Abstract
In this paper, the technique of construction and analysis of quasimonotone finite-difference numerical schemes for scalar conservation laws in one space dimension, developed in Part I [SIAM J. Numer. Anal., 26 (1989), pp. 1325–1341], is extended to a wide class of Petrov–Galerkin finite-element methods. The resulting schemes are called the quasimonotone finite-element schemes. The approximate solution $u_h $ is written as $\bar u_h + \tilde u_h $, where $\bar u_h $ is a piecewise-constant function. The Petrov–Galerkin methods are then considered to be a set of equations that defines “the parameter” $\tilde u_h $, plus a single equation, which is essentially a finite-difference scheme, that defines “the means” $\bar u_h $. All the results of the theory of quasimonotone finite-difference schemes can be carried over this finite-element framework by this simple point of view.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
