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Adaptive Computation of Parameters in Stabilized Methods for Convection-Diffusion Problems

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • V. John

    (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
    Free University of Berlin, Department of Mathematics and Computer Science)

  • P. Knobloch

    (Charles University, Department of Numerical Mathematics,Faculty of Mathematics and Physics)

Abstract

Stabilized finite element methods for convection-dominated problems contain parameters whose optimal choice is usually not known.This paper presents techniques for computing stabilization parameters in an adaptive way by minimizing a target functional characterizing the quality of the approximate solution.This leads to a constrained nonlinear optimization problem.Numerical results obtained for various target functionals are presented.They demonstrate that a posteriori optimization of parameters can significantly improve the quality of solutions obtained using stabilized methods.

Suggested Citation

  • V. John & P. Knobloch, 2013. "Adaptive Computation of Parameters in Stabilized Methods for Convection-Diffusion Problems," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 275-283, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_30
    DOI: 10.1007/978-3-642-33134-3_30
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