An adaptive discontinuous finite volume method for elliptic problems

An adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a mesh-dependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analy...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of computational and applied mathematics 2011-07, Vol.235 (18), p.5422-5431
Hauptverfasser:	Liu, Jiangguo, Mu, Lin, Ye, Xiu
Format:	Artikel
Sprache:	eng
Schlagworte:	a posteriori error estimates Acceleration of convergence Adaptive mesh refinements Computation Convergence Direct power generation Elliptic boundary value problems Error reduction Exact sciences and technology Finite volume method Finite volume methods Mathematical analysis Mathematical models Mathematics Norms Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Sciences and techniques of general use
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	An adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a mesh-dependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analysis. ► An adaptive discontinuous finite volume method (DFVM) is developed. ► The adaptive DFVM achieves guaranteed error reduction. ► The adaptive DFVM is asymptotically optimal as nonlinear approximation.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2011.05.051