Total Flux Estimates for a Finite-Element Approximation of Elliptic Equations
- 1 April 1987
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 7 (2) , 129-148
- https://doi.org/10.1093/imanum/7.2.129
Abstract
An elliptic boundary-value problem on a domain Ω with prescribed Dirichlet data on ΓI ⊆∂Ω is approximated using a finite-element space of approximation power hK in the L2 norm. It is shown that the total flux across ΓI can be approximated with an error of O(hK) when Ω is a curved domain in Rn (n = 2 or 3) and isoparametric elements are used. When Ω is a polyhedron, an O(h2K−2) approximation is given. We use these results to study the finite-element approximation of elliptic equations when the prescribed boundary data on ΓI is the total flux.Keywords
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