Unconditional stability of semi-implicit discretizations of singular\n flows

2017/11/29 by Sören Bartels, Lars Diening, Bartels, Sören +3 · 1 citation
Engineering · Mathematics · #35K55 #65M12 #65M15 #65M60 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1712.03260

openalex publication_date 2017/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A popular and efficient discretization of evolutions involving the singular\np-Laplace operator is based on a factorization of the differential operator\ninto a linear part which is treated implicitly and a regularized singular\nfactor which is treated explicitly. It is shown that an unconditional energy\nstability property for this semi-implicit time stepping strategy holds. Related\nerror estimates depend critically on a required regularization parameter.\nNumerical experiments reveal reduced experimental convergence rates for smaller\nregularization parameters and thereby confirm that this dependence cannot be\navoided in general.\n

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