Rigorous a-posteriori analysis using numerical eigenvalue bounds in a\n surface growth model

2017/08/21 by Christian Nolde, Nolde, Christian, Dirk Blömker +1
Engineering · Mathematics · #35P15 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1708.06322

openalex publication_date 2017/08/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In order to prove numerically the global existence and uniqueness of smooth\nsolutions of a fourth order, nonlinear PDE, we derive rigorous a-posteriori\nupper bounds on the supremum of the numerical range of the linearized operator.\nThese bounds also have to be easily computable in order to be applicable to our\nrigorous a-posteriori methods, as we use them in each time-step of the\nnumerical discretization. The final goal is to establish global bounds on\nsmooth local solutions, which then establish global uniqueness.\n

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