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Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem

  • Pekka NeittaanmäkiEmail author
  • Sergey Repin
Chapter
First Online:
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 15)

Abstract

This paper is concerned with computable error estimates for approximations to a boundary-value problem
$$\mathrm{curl}\ {\mu }^{-1}\mathrm{curl}\ u + {\kappa }^{2}u = j\quad \textrm{ in }\Omega ,$$
where μ > 0 and κ are bounded functions. We derive a posteriori error estimates valid for any conforming approximations of the considered problems. For this purpose, we apply a new approach that is based on certain transformations of the basic integral identity. The consistency of the derived a posteriori error estimates is proved and the corresponding computational strategies are discussed.

Key words

A posteriori estimates the Maxwell equation guaranteed bounds of approximation errors 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland
  2. 2.Department of Applied MathematicsSt. Petersburg State Technical UniversitySt. PetersburgRussia

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