L<sup>2</sup> error estimates for a class of any order finite volume schemes over quadrilateral meshes

Yanping Lin, Min Yang, Qingsong Zou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this paper, we propose a unified L2 error estimate for a class of bi-r finite volume (FV) schemes on a quadrilateral mesh for elliptic equations, where r ≥ 1 is arbitrary. The main result is to show that the FV solution possesses the optimal order L2 error provided that (u, f) ∈ Hr+1 × Hr, where u is the exact solution and f is the source term of the elliptic equation. Our analysis includes two basic ideas: (1) By the Aubin-Nistche technique, the L2 error estimate of an FV scheme can be reduced to the analysis of the difference of bilinear forms and right-hand sides between the FV and its corresponding finite element (FE) equations, respectively; (2) with the help of a special transfer operator from the trial to test space, the difference between the FV and FE equations can be estimated through analyzing the effect of some Gauss quadrature. Numerical experiments are given to demonstrate the proved results.
Original languageEnglish
Pages (from-to)2030-2050
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number4
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Elliptic problems
  • Finite volume methods
  • Gauss quadrature
  • High order
  • L&lt;sup&gt;2&lt;/sup&gt; error estimate
  • Quadrilateral meshes

ASJC Scopus subject areas

  • Numerical Analysis

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