A Two-Grid-Approach to Identification and Control Problems for Partial Differential Equations

  • Volkmar Friedrich
  • Bernd Hofmann
Part of the Progress in Scientific Computing book series (PSC, volume 7)


Both parameter identification and control problems for partial differential equations (PDE) can be treated by minimization of functionals the values of which depend on the unknown parameters or control functions. Each evaluation of these functionals requires an approximate solution of a boundary value or an initial boundary value problem (IBVP) for the PDE. To get an acceptable trade-off between accuracy and the amount of computation, we preferably use a coarse-grid-approximation of the IBVP for minimizing these functionals. Only at a few points of the parameter or control function space a fine-grid-approximation of the IBVP has to be calculated in order to reduce the systematic error created by the coarse grid.

This approach will be illustrated by the hand of parabolic equations, but it seems to be quite general even for large scale identification and control problems.


Control Problem Coarse Grid Partial Differential Equation Initial Boundary Value Problem Radial Temperature Profile 
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

© Birkhäuser Boston 1987

Authors and Affiliations

  • Volkmar Friedrich
  • Bernd Hofmann

There are no affiliations available

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