On error indicators for optimizing parameters in stabilized methods
- 13 Downloads
Numerical solution of convection-dominated problems requires special techniques to suppress spurious oscillations in approximate solutions. Often, stabilized methods are applied which involve user-chosen parameters. These parameters significantly influence the quality of the solution but their optimal choice is usually not known. One possibility is to define them in an adaptive way by minimizing an error indicator characterizing the quality of the approximate solution. A non-trivial requirement on the error indicator is that its minimization with respect to the stabilization parameters should suppress spurious oscillations without smearing layers. In this paper, a new error indicator is introduced and its suitability is tested on two newly proposed benchmark problems for which previously proposed indicators do not provide satisfactory results.
Mathematics Subject Classification (2010)65N30 65N12
Unable to display preview. Download preview PDF.
The work of P. Knobloch and P. Lukáš was supported through the grant No. 16-03230S of the Czech Science Foundation.
- 4.John, V., Knobloch, P.: Adaptive computation of parameters in stabilized methods for convection–diffusion problems. In: Cangiani, A., Davidchack, R.L., Georgoulis, E.H., Gorban, A., Levesley, J., Tretyakov, M.V. (eds.) Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011, pp 275–283. Springer, Berlin (2013)Google Scholar
- 6.Lukáš, P.: A posteriori optimization of parameters in the SUPG method for higher degree FE spaces. In: Knobloch, P. (ed.) Boundary and Interior Layers, Computational and Asymptotic Methods – BAIL 2014, Lect. Notes Comput. Sci. Eng., vol. 108, pp 171–182. Springer (2015)Google Scholar