Numerical Analysis and Scientific Computing Seminar | Charles Parker, Computing H2-conforming finite element approximations without having to implement C1-elements

Postdoctoral Fellow Charles Parker, Mathematical Institute University of Oxford

Abstract: Fourth-order elliptic problems arise in a variety of applications from thin plates to phase separation to liquid crystals. A conforming Galerkin discretization requires a finite dimensional subspace of H2, which in turn means that conforming finite element subspaces are C1-continuous. In contrast to standard H1-conforming C0-elements, C1-elements, particularly those of high order, are less understood from a theoretical perspective and are not implemented in many existing finite element codes. In this talk, we address the implementation of the elements. In particular, we present algorithms that compute C1 finite element approximations to fourth-order elliptic problems and which only require elements with at most C0-continuity. We also discuss preconditioners and illustrate the method on a number of representative test problems.