Magnetism in nanostructures theoretical investigation of clusters and thin films

Abstract

In this thesis, we discuss the a priori estimates for the hp mortar finite element methods applied to linear elliptic and parabolic problems In chapter 2 we discuss the stability and approximation properties of the hp mortar projection operator which are used to find the best approximation estimates we discuss the a priori error estimates for the hp mortar finite elephant method when applied to parabolic initial and boundary value problems in chapter 3 we establish the quasioptimal up to O log p error estimates in L2 and piecewise H1 norms with quasiuniform mesh for the semi discrete methods with an extra regularity assumption of the solution,