Solving approximate cloaking problems using finite element methods

Approximate Methods for Solving Flowshop Problems

Solving elliptic eigenvalue problems on polygonal meshes using discontinuous Galerkin composite finite element methods

In this paper we introduce a discontinuous Galerkin method on polygonal meshes. This method arises from the Discontinuous Galerkin Composite Finite Element Method (DGFEM) for source problems on domains with micro-structures. In the context of the present paper, the flexibility of DGFEM is applied to handle polygonal meshes. We prove the a priori convergence of the method for both eigenvalues an...

Methods for Solving Gas Damping Problems in Perforated Microstructures Using a 2D Finite-Element Solver

We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two ph...

Adaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems

In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...

Stress based finite element methods for solving contact problems: Comparisons between various solution methods

Article history: Received 21 January 2007 Accepted 28 November 2008 Available online 12 January 2009