In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Projected Surface Finite Elements for Elliptic Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
1, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss1/2