Adaptive finite element methods in computational mechanics
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
A unified approach to a posteriori error estimation based on duality error majorants
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
A posteriori error estimation for variational problems with uniformly convex functionals
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A posteriori error analysis for elliptic pdes on domains with complicated structures
Numerische Mathematik
Adaptive finite element methods for nonlinear inverse problems
Proceedings of the 2009 ACM symposium on Applied Computing
Adaptive hp-FEM with dynamical meshes for transient heat and moisture transfer problems
Journal of Computational and Applied Mathematics
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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 and leads to effective computer codes aimed to control errors of approximate solutions obtained by the finite element method which presents now a days the main computational tool in industrial software. Various numerical tests confirming high effectivity of this technology are presented.