Adaptive computation of parameters in stabilized methods for convection-diffusion problems

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.

Keywords

• adaptive computation of parameters
• stabilized methods
• convection-diffusion problems