A higher-order finite element approach to the Kuramoto-Sivashinsky equation

作者：Anders Denis^*; Dittmann Maik; Weinberg Kerstin

来源：Zeitschrift fur Angewandte Mathematik und Mechanik, 2012, 92(8): 599-607.

DOI：10.1002/zamm.201200017

• Kuramoto-Sivashinsky equation
• spatio-temporal chaos
• finite element techniques

The Kuramoto-Sivashinsky equation has emerged as a fundamental evolution equation to describe highly nonlinear physical processes in unstable systems. In general, it constitutes a nonlinear initial-valued problem involving fourth-order spatial derivatives. Finite element solutions for the Kuramoto-Sivashinsky equation are not common because the primal variational formulation of fourth-order operators requires finite element basis functions which are piecewise smooth and globally at least C1-continuous. In this paper a novel B-spline based finite element approach to the solution of the one-dimensional Kuramoto-Sivashinsky equation is presented. Extensive numerical studies of different scenarios in the Kuramoto-Sivashinsky equation will illustrate the quality of our approach.

• 出版日期2012-8