A finite element method for surface PDEs: Matrix properties
A new finite element approach is introduced for the discretization of elliptic partial differential equations (PDEs) on surfaces. The finite element spaces are induced by triangulations of an `outer' domain. Applications are given to two-phase flow problems. The paper analyzes the two-dimensional case and shows that the (effective) spectral condition number of the diagonally scaled mass matrix and the diagonally scaled stiffness matrix behaves like \(h^{-3}|\log h|\) and \(h^{-2}|\log h|,\) respectively, where \(h\) is the meshsize of the outer triangulation. Examples are given.
scientific article; zbMATH DE number 5674536