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

Ingeniería y Ciencia

卷:9

Jorge Mauricio Ruiz Vera¹  Ignacio Mantilla Prada¹ 

[1] Departamento de Matemáticas Universidad Nacional de Colombia;

关键词: Finite elements;    Nonlinear evolution equations;    Semiconductors;   

DOI  :  10.17230/ingciecia.9.17.5

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown