Abstract
A posteriori error estimation plays an important role in the modern numerical analysis. The direction from which this topic initially started was the estimation of the computational error in global (energy) norm. Concerning various approaches for this type of estimation we refer to works [1], [2], [3], [4], [5], [6], [13], [15], [16], [17], [18]. For approximations of linear elliptic problems, they examine error estimates in the global (energy) norm and suggest error indicators/estimators that are further used in various mesh adaptive procedures (see, e.g., [10]). Global error estimates give a general presentation on the quality of an approximate solution and a stopping criteria.
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References
M. Ainsworth, J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis, John Wiley & Sons, Inc., New York, 2000.
I. Babuška, W. C. Rheinbold, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978), 736–754.
I. Babuška, W. C. Rheinbold, A posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12 (1978), 1597–1615.
I. Babuška, T. Strouboulis, The Finite Element Method and its Reliability, Oxford University Press Inc., New York, 2001.
W. Bangerth, R. Rannacher, Adaptive finite element methods for differential equations, Lectures in Mathematics ETH Zürich, Birkhäuser-Verlag, Basel, 2003.
R. E. Bank, A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985), 283–301.
R. Becker, R. Rannacher, Weighted a posteriori error control in finite element methods, Preprint 96-1, SFB 359, Heidelberg, 1996.
R. Becker, R. Rannacher, A feed-back approach to error control infinite element methods: Basic approach and examples, East-West J. Numer. Math. 4 (1996), 237–264.
I. Hlaváček, M. Křížek, On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary conditions, Apl. Mat. 32 (1987), 131–154.
S. Korotov, M. Křížek, Global and local refinement techniques yielding nonobtuse tetrahedral partitions, Comput. Math. Appl. (to appear).
S. Korotov, P. Neittaanmäki, and S. Repin, A posteriori error estimation of goal-oriented quantities by the superconvergence patch recovery, J. Numer. Math. 11 (2003), 33–59.
M. Křížek, P. Neittaanmäki, Superconvergence phenomenon in the finite element method arising from averaging gradients, Numer. Math. 45 (1984), 10–116.
P. Ladevéze, D. Leguillon, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal. 20 (1983), 485–509.
J. T. Oden, S. Prudhomme, Goal-oriented error estimation and adaptivity for the finite element method, Comput. Math. Appl. 41 (2001), 735–756.
S Repin, A unified approach to a posteriori error estimation based on duality error majorants, Math. Comput. Simulation 50 (1999), 305–321.
S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals, Math. Comp. 69 (2000), 481–500.
R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, 1996.
O. C. Zienkeiewicz, J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg. 24 (1987), 337–357.
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Neittaanmäki, P., Korotov, S., Martikainen, J. (2004). A Posteriori Error Estimation of “Quantities of Interest” on “Quantity-Adapted” Meshes. In: Křížek, M., Neittaanmäki, P., Korotov, S., Glowinski, R. (eds) Conjugate Gradient Algorithms and Finite Element Methods. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18560-1_11
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