A priori error analysis of the hp mortar finite element methods for elliptic and parabolic problems

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, newlinewe establish the superconvergence estimates in negative norms. We obtain exponential newlinedecay of the error in the spatial direction when a proper combination newlineof meshes and polynomial degrees are chosen. Further, we analyzed newlinea fully discrete scheme using the backward Euler finite difference in newlinethe temporal direction and obtain the quasioptimal order estimates newlinein space and first order estimates in time.