A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation

• Main Authors: Jorge Mauricio Ruiz Vera, Ignacio Mantilla Prada
• Format: Article
• Language: English
• Published: Universidad EAFIT 2013-03-01
• Series: Ingeniería y Ciencia
• Subjects: Finite elements; Nonlinear evolution equations; Semiconductors
• Online Access: http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1737

The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented. MSC: 35G25, 65M60, 82D37