Abstrakt
Multilevel methods compute approximate solutions of a problem using its formulation on different levels. The approximate solutions are computed using smoothing on fine levels and solving on the coarsest level.
The analysis of multilevel methods is typically carried out under the assumption that the problem on the coarsest level is solved exactly. This assumption is, however, not satisfied in practical computations due to the use of an iterative solver on the coarsest level, finite precision arithmetic, or both.
In this talk, I will briefly present the results from my master thesis in which we studied convergence behavior of multilevel methods with inexact solver on the coarsest level. Further, I will describe our current research in which we focus on residual-based error estimates for the total error in multilevel frameworks.
Our goal is to describe connections between estimates presented in literature and derive generalized results. In the end, I will touch on the topics I would like to study in the future such as the use of recycled Krylov methods as the solver on the coarsest level, stopping criteria for iterative solvers on the coarsest level, or effects of finite precision arithmetic.