Numerical exploration of a forward-backward diffusion equation

2010/08/30 by Pauline Lafitte, Corrado Mascia, Lafitte, Pauline +1
Computer Science · Mathematics · #35K70 #47J40 #65M30 #80A22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1008.5108

openalex publication_date 2010/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of a third-order pseudo-parabolic equation. Precisely, we propose schemes for both the second and the third order equations, we discuss the analytical properties of their semi-discrete counter-parts and we compare the numerical results in the case of initial data of Riemann type, showing strengths and flaws of the two approaches, the main emphasis being given to the propagation of transition interfaces.

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