A Decomposition Method for Some Biharmonic Problems

Abstract

In this paper we consider two biharmonic problems [13] which will be conventionally indicated as "simply supported" and "clamped plate" problem.
We construct a decomposition method [16], [19] related to the partition of the plate in two, or more, subdomains. We carry on the numerical treatment of the method first decoupling these fourth order problems into two second order problems, then discretizing these problems by mixed linear finite element and obtaining an algebraic system. Moreover,  we present an iterative block algorithm for solving the foregoing system, which can be efficiently developed on parallel computers.
In the end, we extend the method to the respective biharmonic variational inequalities [10].