Virtual Element Methods for three-dimensional Hellinger-Reissner elastostatic problems

Generalized ®nite element methods for three-dimensional structural mechanics problems

The present paper summarizes the generalized ®nite element method formulation and demonstrates some of its advantages over traditional ®nite element methods to solve complex, three-dimensional (3D) structural mechanics problems. The structure of the sti€ness matrix in the GFEM is compared to the corresponding FEM matrix. The performance of the GFEM and FEM in the solution of a 3D elasticity pro...

A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems

A new fast multipole boundary element method (BEM) is presented in this paper for large-scale analysis of two-dimensional (2-D) elastostatic problems based on the direct boundary integral equation (BIE) formulation. In this new formulation, the fundamental solution for 2-D elasticity is written in a complex form using the two complex potential functions in 2-D elasticity. In this way, the multi...

Dd Methods for Three - Dimensional Thermoelastic Problems

Conforming and Nonconforming Virtual Element Methods for Elliptic Problems

We present, in a unified framework, new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H1and L2-err...

Schwarz Methods of Neumann-neumann Type for Three-dimensional Elliptic Finite Element Problems

Several domain decomposition methods of Neumann-Neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by nite elements. We will only consider problems in three dimensions. Several new variants of the basic algorithm are introduced in a Schwarz method framework that provides tools which have already proven ver...