Article thumbnail

A MODIFIED CHARACTERISTIC FINITE ELEMENT METHOD FOR A FULLY NONLINEAR FORMULATION OF THE SEMIGEOSTROPHIC FLOW EQUATIONS

By Xiaobing Feng and Michael Neilan

Abstract

This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Ampére equation and a transport equation. The system is the Eulerian formulation in the dual space for the B. J. Hoskins ’ semigeostrophic flow equations, which are widely used in meteorology to model slowly varying flows constrained by rotation and stratification. To overcome the difficulty caused by the strong nonlinearity, we first formulate (at the differential level) a vanishing moment approximation of the semigeostrophic flow equations, a methodology recently proposed by the authors [17, 18], which involves approximating the fully nonlinear Monge-Ampére equation by a family of fourth order quasilinear equations. We then construct a fully discrete modified characteristic finite element method for the regularized problem. It is shown that under certain mesh and time stepping constraints, the proposed numerical method converges with an optimal order rate of convergence. In particular, the obtained error bounds show explicit dependence on the regularization parameter ε. Numerical tests are also presented to validate the theoretical results and to gauge the efficiency of the proposed fully discrete modified characteristic finite element method

Topics: Key words. semigeostrophic flow, fully nonlinear PDE, viscosity solution, modified characteristic method
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.243.8711
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://arxiv.org/pdf/0810.1479... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.