Diffusion of tangential tensor fields: numerical issues and influence of geometric properties

Abstract

We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods differ with respect to the surface representation used, the geometric information required, and the treatment of the tangentiality condition. We emphasize the importance of geometric properties and their increasing influence as the tensorial degree changes from n=0 to n>=1. A specific example is presented that illustrates how curvature drastically affects the behavior of the solution.

arXiv comment25 pages, 6 figures

References in corpus (8)

• A finite element approach for vector- and tensor-valued surface PDEs
• Orientational order on surfaces - the coupling of topology, geometry, and dynamics
• Analysis of Finite Element Methods for Vector Laplacians on Surfaces
• Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
• Divergence-free tangential finite element methods for incompressible flows on surfaces
• The Hellan-Herrmann-Johnson Method for Nonlinear Shells
• Dune-CurvedGrid -- A Dune module for surface parametrization
• Tangential Errors of Tensor Surface Finite Elements