By Repin, Sergey
This booklet bargains with the trustworthy verification of the accuracy of approximate options that's one of many primary difficulties in glossy utilized analysis. After giving an outline of the tools constructed for types in line with partial differential equations, the writer derives computable a posteriori blunders estimates through the use of equipment of the idea of partial differential equations and useful research. those estimates are appropriate to approximate suggestions computed via a variety of equipment.
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Additional info for A Posteriori Estimates for Partial Differential Equations (Radon Series on Computational and Applied Mathematics)
Rappaz [264, 265] and R. , see [355, 356]). The book  contains a systematic consideration of this question. Certain particular classes of nonlinear problems were analyzed by many authors. For example, nonlinear diffusion-convection problems were considered in J. Medina, M. Picasso and J. Rappaz  and for nonlinear parabolic problems in R. Verf¨urth . A posteriori estimates for variational inequalities related to problems with obstacles were analyzed in M. Ainsworth, J. T. Oden, and C.
Rannacher , K. Eriksson, D. Estep, P. Hansbo and C. Johnson , and R. Verf¨urth . There, the reader will find detailed expositions of various approaches, results of numerical experiments, and a wide list of references. Below, 32 Chapter 2 Overview we shortly discuss several a posteriori error estimation methods developed for finite element approximations. Certainly, the exposition is not complete. Its goal is to give a view of the mathematical ideas underlying the methods. 1 Explicit residual methods From the mathematical viewpoint, the classical “residual method” is a method for finding an upper bound of the residual functional evaluated in the topology of the image space of the respective operator.
To J. -S. Chow, G. F. Carey and R. D. Lazarov , R. E. Ewing, R. D. Lazarov and J. Wang , I. Hlav´ac˘ ek and M. K˘ri˘zek , M. Kˇr´ızˇ ek and P. Neittaanm¨aki [202, 242], R. Lazarov , R. Verf¨urth , J. Wang , J. Wang and X. -E. Wiberg, F. Abdulwahab and S. Ziukas , Z. Zhang and A. Naga , and in many other publications. In L. Wahlbin  readers can find a detailed exposition of the subject and other references. , in M. Kˇr´ızˇ ek and P. Neittaanm¨aki , J.