Abstract

RUIZ VERA, Jorge Mauricio  and  MANTILLA PRADA, Ignacio. A Fully Discrete Finite Element Scheme for the Derrida-Lebowitz-Speer-Spohn Equation. ing.cienc. [online]. 2013, vol.9, n.17, pp.97-110. ISSN 1794-9165.

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 finite element discretization for a exponential formulation of 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 the 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.

Keywords : Finite elements; Nonlinear evolution equations; Semiconductors.

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