Staircasing in semidiscrete stabilised inverse diffusion algorithms

Abstract

We consider a semidiscrete model problem for the approximation of stabilised inverse linear diffusion processes. The work is motivated by an important observation on fully discrete schemes concerning the so-called staircasing phenomenon: when sharpering montone data profiles, fully discrete methods generally introduce stepfunction-type solutions reminding of staircases. In this work, we show by an analysis of dynamical systems in corresponding semidiscrete formulations, that already the semidiscrete numerical model contains the relevant information on the occurrence of staircasing. Numerical experiments confirm and complement the theoretical results.