Li Tian, University of South Carolina


Analysis of a Mixed Finite Volume Discretization of Fourth Order Equations on General Surfaces

Abstract:  Classical finite volume methods do mesh generation and solve equations on a 2D plane, while numerical solutions of PDEs on arbitrary surfaces are needed in diverse applications such as fluid dynamics, weather forecast and climate modeling, cell membrane and image processing. In this paper, we discuss how to solve a Fourth Order Ellipse Equation on arbitrary surface with Mixed Finite Volume Discretization, analysis and convergence rate, and numerical experiment is given after the theoritical part.

Advisor: Lili Ju (USC)