Stabilized approximation to degenerate transport equations via filtering

摘要

We analyze a stabilization technique for degenerate transport equations. Of particular interest are coupled parabolic/hyperbolic problems, when the diffusion coefficient is zero in part of the domain. The unstabilized, computed approximations of these problems are highly oscillatory, and several techniques have been proposed and analyzed to mitigate the effects of the sub-grid errors that contribute to the oscillatory behavior. In this paper, we modify a time-relaxation algorithm proposed in [1] and further studied in [10]. Our modification introduces the relaxation operator as a post-processing step. The operator is not time-dependent, so the discrete (relaxation) system need only be factored once. We provide convergence analysis for our algorithm along with numerical results for several model problems.