Numerical Analysis of the Intrinsic Surface Finite Element Method for Linear Parabolic PDEs on Evolving Surfaces

This thesis presents the formulation and the numerical analysis of the Intrinsic Surface Finite Element Method (EISFEM) on evolving surfaces for the Diffusion Equation (the main representative of linear parabolic second order Partial Differential Equations). The numerical analysis is carried out by a continuous comparison with the analogous coming from the well-established Surface Finite Element Method on evolving surfaces (ESFEM). The Finite Element formulation presented in the thesis takes advantage of the existence of a smooth parametrization for the evolving surface, which is one of the main hypothesis of this work. With respect to classical ESFEM, this approach allows to treat with more precision the geometry of the surface, introducing approximations only at the level of quadrature rules. Finally several experimental results are presented in order to validate the whole dissertation and compare EISFEM results with the ones displayed in literature for ESFEM.