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Total flux estimates for a finite-element approximation of elliptic equations. (English) Zbl 0619.65098
Authors’ summary: An elliptic boundary-value problem on a domain \(\Omega\) with prescribed Dirichlet data on \(\Gamma_ I\subseteq \partial \Omega\) is approximated using a finite-element space of approximation power \(h^ K\) in the \(L^ 2\) norm. It is shown that the total flux across \(\Gamma_ I\) can be approximated with an error of \(O(h^ K)\) when \(\Omega\) is a curved domain in \({\mathbb{R}}^ n\) \((n=2\) or 3) and isoparametric elements are used. When \(\Omega\) is a polyhedron, an \(O(h^{2K-2})\) approximation is given. We use these results to study the finite-element approximation of elliptic equations when the prescribed boundary data on \(\Gamma_ I\) is the total flux.
Reviewer: R.D.Westbrook

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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