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Bartels, S.; Carstensen, C.; Dolzmann, G.

Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. (English) Zbl 1062.65113

Numer. Math. 99, No. 1, 1-24 (2004).
The authors study the influence of approximation errors in the Dirichlet boundary data for finite element approximations of elliptic partial differential equations. Quantitative a priori and a posteriori estimates are presented for the nodal interpolation and the \( L^2 \) orthogonal projections. It is observed that the \( L^2 \) projetion of the given Dirichlet data onto the trace space of the finite element functions on the boundary gives always higher order contributions in posteriori estimates than the nodal interpolation (cf. C. Carstensen and S. Bartels [Math. Comp. 71, 945–969 (2002; Zbl 0997.65126)]).
Reviewer: H. P. Dikshit (New Delhi)

Cited in 42 Documents

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

finite element approximation; Dirichlet boundary data; elliptic partial differential equations; a posteriori error estimates

Citations:

Zbl 0997.65126
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Full Text: DOI

References:

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