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Overview of Other Results and Open Problems

  • Chapter
Accuracy Verification Methods

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 32))

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Abstract

This chapter presents an overview of results related to error control methods, which were not considered in previous chapters. In the first part, we discuss possible extensions of the theory exposed in Chaps. 3 and 4 to nonconforming approximations and certain classes of nonlinear problems. Also, we shortly discuss some results related to explicit evaluation of modeling errors. The remaining part of the chapter is devoted to a posteriori estimates of errors in iteration methods. Certainly, the overview is not complete. A posteriori error estimation methods are far from having been fully explored and this subject contains many unsolved problems and open questions, some of which we formulate in the last section.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Olli Mali & Pekka Neittaanmäki

  2. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

    Sergey Repin

  3. University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

Authors
  1. Olli Mali
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  2. Pekka Neittaanmäki
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  3. Sergey Repin
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Mali, O., Neittaanmäki, P., Repin, S. (2014). Overview of Other Results and Open Problems. In: Accuracy Verification Methods. Computational Methods in Applied Sciences, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7581-7_6

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  • DOI: https://doi.org/10.1007/978-94-007-7581-7_6

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