Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations. (5th January 2018)

• Record Type: Journal Article
• Authors: Erath, Christoph; Praetorius, Dirk
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 2(2019)
• Page Start: 983
• Page End: 1008
• Publication Date: 2018-01-05
• Subjects: finite volume method -- Céa-type quasi-optimality -- a posteriori error estimators -- adaptive algorithm -- local mesh refinement -- optimal convergence rates -- nonsymmetric problems; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry006
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We prove optimal convergence rates for the discretization of a general second-order linear elliptic partial differential equation with an adaptive vertex-centered finite volume scheme. While our prior work Erath & Praetorius (2016, Adaptive vertex-centered finite volume methods with convergence rates. SIAM J. Numer. Anal., 54, 2228–2255) was restricted to symmetric problems, the present analysis also covers nonsymmetric problems and hence the important case of present convection.