Mats Larson
Department of Mathematics and Mathematical Statistics
Umeå University
Umeå
In this talk we give an introduction to finite element approximation of PDEs on surfaces. We consider a wide range of problems, which are relevant in applications, including the Laplace-Beltrami problem, the biharmonic problem, the Darcy problem, the Stokes problem, and the Membrane problem. We present the basic approach to deriving a priori error estimates, which takes the approximation of the geometry as well as the solution into account. We also develop an approach for solving finite element approximation of PDEs on so called composite surfaces that consists of an arrangement of surfaces with applications to problems on surfaces with sharp edges and corners and intersecting surfaces.