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A posteriori error estimation of goal-oriented quantities for elliptic type BVPs. (English) Zbl 1089.65120

Summary: In practice the process or object under analysis is usually modelled by means of a selected mathematical model, whose approximate solution is computed with a help of a certain computer code. This approximate solution necessarily includes various errors related to the approximation itself, special features of the particular method used, round-off errors, etc. Therefore, it inevitably rises the question about the reliability of the computed approximations.
In the present paper we describe and test numerically the new effective computational technology designed for a control of the accuracy of approximate solutions in terms of goal-oriented quantities (or goal-oriented criteria). Such quantities are to be chosen by a user depending on solution properties that present a special interest. The technology proposed is applicable to the elliptic type boundary-value problems (BVPs) and leads to effective computer codes aimed to control errors of approximate solutions obtained by the finite element method which presents nowadays the main computational tool in industrial software. Various numerical tests confirming high effectivity of this technology are presented.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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