Overview of Other Results and Open Problems

  • Olli Mali
  • Pekka Neittaanmäki
  • Sergey Repin
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 32)


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.


Variational Inequality Optimal Control Problem Iteration Method Posteriori Error Posteriori Error Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Olli Mali
    • 1
  • Pekka Neittaanmäki
    • 1
  • Sergey Repin
    • 2
    • 3
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland
  2. 2.Steklov Institute of MathematicsRussian Academy of SciencesSt. PetersburgRussia
  3. 3.University of JyväskyläJyväskyläFinland

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