Computing and Visualization in Science

, Volume 13, Issue 5, pp 221–228

A generalization of the vertex-centered finite volume scheme to arbitrary high order


DOI: 10.1007/s00791-010-0139-z

Cite this article as:
Vogel, A., Xu, J. & Wittum, G. Comput. Visual Sci. (2010) 13: 221. doi:10.1007/s00791-010-0139-z


A higher order finite volume method for elliptic problems is proposed for arbitrary order \({p \in \mathbb{N}}\) . Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in the H1-norm. The error in the L2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees.


Finite volume methodVertex-centeredHigher order

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Goethe Center for Scientific Computing (G-CSC)Goethe-University Frankfurt am MainFrankfurt am MainGermany
  2. 2.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA