An Additive Neumann-Neumann Method for Mortar Finite Element for 4th Order Problems (original) (raw)

A FETI-DP Method for Mortar Finite Element Discretization of a Fourth Order Problem

In this paper we present a FETI-DP type algorithm for solving the system of algebraic equations arising from the mortar finite element discretization of a fourth order problem on a nonconforming mesh. A conforming reduced Hsieh-Clough-Tocher macro element is used locally in the subdomains. We present new FETI-DP discrete problems and later introduce new parallel preconditioners for two cases: where there are no crosspoints in the coarse division of subdomains and in the general case.

19. A Mortar Finite Element Method for Plate Problems

2001

This paper is concerned with the mortar method where locally in the subdomainsthe nonconforming Adini and Morley plate finite elements are used. We restrict ourselvesto the geometrically conforming version of the mortar method, i.e. the localsubstructures form a coarse triangulation. We first introduce independent local discretizationsfor the two discussed elements in each subdomain. The 2-D triangulationsof two neighboring subregions do

A balancing Neumann–Neumann method for a mortar finite element discretization of a fourth order elliptic problem

Journal of Numerical Mathematics, 2010

In the paper a balanced Neumann-Neumann algorithm for the reduced HCT finite element nonmatching meshes is discussed. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions. The algorithms are analyzed using the abstract Schwarz framework, proving an almost optimal condition bound which is independent of the parameters of the problem, and depends only logarithmically on the ratio between the subdomain size and the mesh size.

A mortar element method for some discretizations of a plate problem

Numerische Mathematik, 2002

In this paper mortar element methods for the clamped plate problem are discussed. Locally, we use conforming Hsieh-Clough-Tocher (HCT) and reduced HCT macro elements and a nonconforming Morley element. We establish error bounds for these methods.

An Iterative Substructuring Method for Mortar Nonconforming Discretization of a Fourth-Order Elliptic Problem in Two Dimensions

Lecture Notes in Computational Science and Engineering

In this paper we consider an iterative substructuring method for solving system of equations arising from mortar Morley finite element discretization of a model fourth order elliptic problem in 2D. The parallel preconditioner for the interface problem is introduced using Additive Schwarz Method framework. The method is quasi-optimal i.e. the number of CG iterations for the preconditioned problem grows polylogarithmically as the sizes of the meshes decrease and it is independent of the jumps of the coefficients.

A Hierarchical Preconditioner for the Mortar Finite Element Method

Electronic Transactions on Numerical Analysis, 1995

Mortar elements form a family of nonconforming finite element methods that are more flexible than conforming finite elements and are known to be as accurate as their conforming counterparts. A fast iterative method is developed for linear, second order elliptic equations in the plane. Our algorithm is modeled on a hierarchical basis preconditioner previously analyzed and tested, for the conforming case, by Barry Smith and the second author. A complete analysis and results of numerical experiments are given for lower order mortar elements and geometrically conforming decompositions of the region into subregions.