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

Andreas Vogel, Jinchao Xu, Gabriel Wittum

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A higher order finite volume method for elliptic problems is proposed for arbitrary order p ∈ 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 H 1-norm. The error in the L 2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees.

Original languageEnglish (US)
Pages (from-to)221-228
Number of pages8
JournalComputing and Visualization in Science
Volume13
Issue number5
DOIs
StatePublished - Jun 2010

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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