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Kornhuber, R.

A posteriori error estimates for elliptic variational inequalities. (English) Zbl 0857.65071

Comput. Math. Appl. 31, No. 8, 49-60 (1996).
A posteriori error estimates play a crucial role in the approximative solution of partial differential equations by adaptive finite element methods. In the paper, the author describes a hierachical error estimate which results from the following two steps: (i) Discretize the defect problem with respect to an enlarged space. (ii) Localize the discrete defect problem by domain decomposition.
This method reduces the evaluation amounts to the solution of corresponding scalar local subproblems. Some upper bounds for the effectivity rates and the numerical properties of the method are derived and illustrated by typical examples.
Reviewer: J.Vaníček (Praha)

Cited in 26 Documents

MSC:

65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49J40 Variational inequalities
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)

Keywords:

elliptic variational inequalities; free boundary problem; numerical examples; error estimates; finite element methods; domain decomposition

Software:

PLTMG
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\textit{R. Kornhuber}, Comput. Math. Appl. 31, No. 8, 49--60 (1996; Zbl 0857.65071)
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References:

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