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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
##### Keywords:
flux estimates; finite element method; eror estimates
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