Download e-book for iPad: A Posteriori Estimates for Partial Differential Equations by Repin, Sergey

By Repin, Sergey

ISBN-10: 3110191539

ISBN-13: 9783110191530

This publication bargains with the trustworthy verification of the accuracy of approximate strategies that's one of many vital difficulties in smooth utilized analysis. After giving an summary of the tools built for types in accordance with partial differential equations, the writer derives computable a posteriori blunders estimates by utilizing equipment of the idea of partial differential equations and useful research. those estimates are acceptable to approximate recommendations computed by way of a variety of tools.

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Extra info for A Posteriori Estimates for Partial Differential Equations (Radon Series on Computational and Applied Mathematics)

Sample text

Bank and A. Weiser [42]) error indicators are constructed with the help of local boundary value problems with data defined by residuals and interelement jumps (see also R. Duran and R. Rodriguez [119]). , see M. Ainsworth and J. T. Oden [8]), local boundary value problems are constructed on each element, using the residuals and suitable Neumann conditions on boundaries of the elements. Local Dirichlet and Neumann problems on patches are also used in E. Stein and S. Ohnimus [339] and R. Verf¨urth [358, 360].

Brady and A. R. Elcrat [66]. Adaptive methods for convection-diffusion problems are considered in C. Johnson [186] and R. Verf¨urth [360]. Papers by R. Verf¨urth [359] and K. Eriksson and C. Johnson [126] are devoted to parabolic type problems. A posteriori error estimates for anisotropic meshes are presented in K. G. Siebert [334] and G. Kunert [203, 204]. Also, we recommend papers by I. Babuˇska, R. Duran, and R. Rodriguez [25], G. F. Carey and D. L. Humphrey [84], J. T. Oden, L. Demkowicz, W.

A. Funken [92, 93] (in these papers the authors consider ways of computing bounds of interpolation constants in the residual based error estimator), C. Carstensen and R. Verf¨urth [100] (the authors show that the “edge component” dominates in the residual error estimator), K. Eriksson and C. Johnson [125], and C. Johnson and P. Hansbo [187]. In C. Carstensen and S. Sauter [99], a posteriori error estimates were derived for elliptic PDEs on domains with complicated structures. Estimates for problems with biharmonic operator are analyzed in A.

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A Posteriori Estimates for Partial Differential Equations (Radon Series on Computational and Applied Mathematics) by Repin, Sergey

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