ISSN:
0945-3245
Schlagwort(e):
AMS(MOS): 65 N 30
;
CR: G1.8
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Summary This paper considers the finite element approximation of the semi-definite Neumann problem: −∇·(σ∇u)=f in a curved domain Ω⊂ℝ n (n=2 or 3), $$\sigma \frac{{\partial u}}{{\partial v}} = g$$ on πΩ and $$\int\limits_\Omega {u dx} = q$$ , a given constant, for dataf andg satisfying the compatibility condition $$\int\limits_\Omega {f dx} + \int\limits_{\partial \Omega } {g ds} = 0$$ . Due to perturbation of domain errors (Ω→Ω h ) the standard Galerkin approximation to the above problem may not have a solution. A remedy is to perturb the right hand side so that a discrete form of the compatibility condition holds. Using this approach we show that for a finite element space defined overD h , a union of elements, with approximation powerh k in theL 2 norm and with dist (Ω, Ω h )≦Ch k , one obtains optimal rates of convergence in theH 1 andL 2 norms whether Ω h is fitted (Ω h ≡D h ) or unfitted (Ω h ⊂D h ) provided the numerical integration scheme has sufficient accuracy.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01399693
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