An Adaptive Surface Finite Element Method for the Laplace-Beltrami Equation

Abstract: In this thesis, we present an adaptive surface finite element method for the Laplace-Beltrami equation. The equation is known as the manifold equivalent of the Laplace equation. A surface finite element method is formulated for this partial differential equation which is implemented in FEniCS, an open source software project for automated solutions of differential equations. We formulate a goal-oriented adaptive mesh refinement method based on a posteriori error estimates which are established with the dual-weighted residual method. Some computational examples are provided and implementation issues are discussed.