Analytic regularity for a singularly perturbed fourth order reaction-diffusion boundary value problem

2023/11/12 by P. Constantinou, Constantinou, P., Christos Xenophontos +1
Mathematics · #65L11 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2311.06849

openalex publication_date 2023/11/12 · openalex created_date 2023/11/16 · openalex updated_date 2026/07/28

Abstract

We consider a fourth order, reaction-diffusion type, singularly perturbed boundary value problem, and the regularity of its solution. Specifically, we provide estimates for arbitrary order derivatves, which are explicit in the singular perturbation parameter as well as the differentiation order. Such estimates are needed for the numerical analysis of high order methods, e.g.hp Finite Element Method (FEM).

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