Workshop singulär gestörter Probleme
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A posteriori computation of parameters in stabilized methods for convection-diffusion problems
This contribution is devoted to the numerical solution of convection dominated convection-diffusion equations by means of the finite element method. Standard discretizations of such problems lead to solutions that are globally polluted by large spurious oscillations. In practice, stabilized methods are used that often include so-called stabilization parameters. The values of the stabilization parameters significantly influence the quality of the discrete solution but, usually, it is not known how the parameters should be defined.
We propose to compute the stabilization parameters a posteriori by minimizing a suitable target functional, which leads to a nonlinear constraint optimization problem. We formulate a general framework for the optimization of parameters in stabilized methods for convection-diffusion equations and discuss the choice of appropriate target functionals. Benefits of our approach are demonstrated by means of numerical results.