On Mortar-type Incomplete Biquadratic Plate Element For Plate Problem

This thesis discusses the Mortar finite element method, introduced by Bernardi-Maday-Patera (1994). The Mortar finite elements methods are particularly useful whiledesigning complex structural components (e.g. wing and fuselage) which may havebeen modeled by di?erent analysts. This often requires several individual subdomains.In such case, it is often too cumbersome, or even infeasible, to coordinate the meshover separate components such that they are conforming at interfaces. And with thedevelopment of parallel computers in recent years, there has been growing interest innonoverlapping domain decomposition methods coupling di?erent variational approx-imations in di?erent subdomains. Hence, one needs to seek help of non-conforming(Mortar) techniques.On the subdomains of the Mortar method one can use the locally conformingelements and also can use locally nonconforming elements. In this thesis we consider aMortar element with locally nonconforming elements for solving plate bending problem.In the subdomains, the incomplete biquadratic plate elements are used. For Poissonequation, there is one Mortar condition at the interfaces: the solution in projectionway. In this thesis, there are two Mortar conditions for plate bending problem: oneis for the solution itself in pointwise way, the other is for the normal derivative of thesolution in the projection way. In this way, we can keep the global convergence of thismethod.After detail analysis, an error estimate in energy norm is obtained, which is opti-mal in approximation order and only requires the regularity just like that for Morleyelement method(Huang J G, Li L K, Chen J R reference as in the article On mortar-typeMorley element method for plate bending problem): u∈H3(?)∩H02(?), f∈L2(?).At the end of the thesis, there is a numerical example of the Mortar method.