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Repin, S.; Valdman, J.

Functional a posteriori error estimates for problems with nonlinear boundary conditions. (English) Zbl 1146.65054

J. Numer. Math. 16, No. 1, 51-81 (2008).
Summary: We consider variational inequalities related to problems with nonlinear boundary conditions. We are focused on deriving a posteriori estimates of the difference between exact solutions of such type variational inequalities and any function lying in the admissible functional class of the problem considered. These estimates are obtained by an advanced version of the variational approach earlier used for problems with uniformly convex functionals.
It is shown that the structure of error majorants reflects properties of the exact solution. The majorants provide guaranteed upper bounds of the error for any conforming approximation and possess necessary continuity properties. In the series of numerical tests performed, it was shown that the estimates are explicitly computable, provide sharp bounds of approximation errors, and give high quality indication of the distribution of local (elementwise) errors.

Cited in 9 Documents

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M25 Discrete approximations in optimal control

Keywords:

functional a posteriori error estimates; nonlinear boundary conditions; variational inequalities; friction type conditions; numerical examples
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\textit{S. Repin} and \textit{J. Valdman}, J. Numer. Math. 16, No. 1, 51--81 (2008; Zbl 1146.65054)
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References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.