The Finite Volume Element Method for Diffusion Equations on General Triangulations Journal Article uri icon

Overview

abstract

  • This paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in $mathcal{R}^2 $ using a special type of control volume. The theory applies to diffusion equations of the form [ begin{gathered} - nabla (Anabla u) = fquad {text{in }}Omega , hfill \ u = 0quad {text{on }}partial Omega . hfill \ end{gathered} ] Under fairly general conditions, the theory establishes $O(h)$ estimates of the error in a discrete $mathcal{H}^1 $ seminorm. Under an additional assumption concerning local uniformity of the triangulation, the estimate is improved to $O(h^2 )$.

publication date

  • April 1, 1991

has restriction

  • closed

Date in CU Experts

  • September 17, 2013 7:59 AM

Full Author List

  • Cai Z; Mandel J; McCormick S

author count

  • 3

Other Profiles

International Standard Serial Number (ISSN)

  • 0036-1429

Electronic International Standard Serial Number (EISSN)

  • 1095-7170

Additional Document Info

start page

  • 392

end page

  • 402

volume

  • 28

issue

  • 2