The Residual-Free-Bubble Finite Element Method on Anisotropic Partitions

The Residual-Free-Bubble Finite Element Method on Anisotropic Partitions

The subject of this work is the analysis and implementation of stabilized finite element methods on anisotropic meshes. We develop the anisotropic a priori error analysis of the residual-free-bubble (RFB) method applied to elliptic convection-dominated convection-diffusion problems in two dimensions, with finite element spaces of type Qk, k ≥ 1. In the case of P1 finite elements, relying on the...

Stability of the Residual Free Bubble Method for Bilinear Finite Elements on Rectangular Grids

The Residual–Free Bubble Method for Problems with Multiple Scales

The Residual–Free Bubble Method for Problems with Multiple Scales Andrea Cangiani St Hugh’s College Doctor of Philosophy Trinity Term 2004 This thesis is devoted to the numerical analysis and development of the residual–free bubble finite element method. We begin with an overview of known results and properties of the method, showing how techniques used on a range of multiscale problems can be ...

Enhanced residual–free bubble method for convection–diffusion problems

We analyse the performance of the enhanced residual–free bubble (RFBe) method for the solution of convection–dominated convection–diffusion problems in 2–D, and compare the present method with the standard residual–free bubble (RFB) method. The advantages of the RFBe method are two folded: it has better stability properties and it can be used to resolve boundary layers with high accuracy on glo...

Anisotropic adaptive finite element method for modelling blood flow.

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velo...