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 counterparts 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.
NUMERICAL EXPLORATION OF A FORWARD-BACKWARD DIFFUSION EQUATION / P., Lafitte; Mascia, Corrado. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 22:6(2012), pp. 1250004-.... [10.1142/s0218202512500042]
NUMERICAL EXPLORATION OF A FORWARD-BACKWARD DIFFUSION EQUATION
MASCIA, Corrado
2012
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 counterparts 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.