A new volume deformation technique using FEM and voxel-texture (voxture) maps has been developed. In contrast to the traditional deformation techniques, the new algorithm is aimed at volume transformations, deformations and volume metamorphosis.

Abstract. A semidiscrete finite volume element (FVE) approximation to a parabolic integrodifferential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimalorder L2-error estimate for smooth initial data and nearly the same optimal-order L2-error estimate for nonsmooth initial data are obtained. More precisely, for homogeneous equations, an elementary energy techni...

We examine a cell-vertex finite volume method which is applied to a model parabolic convection-diffusion problem. By using techniques from finite element analysis, local errors away from all layers are obtained in a seminorm that is related to, but weaker than, the L2 norm.

Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order interpolation for displacement and variables. In particular, use linear finite elements to discretize both stress equilibrium equations is widespread in literature. However, P1 Lagrange shape functions model not optimal, as latter contains cusps full...

In this paper, we present an overview of the progress of the finite volume element (FVE) methods. We show that the linear FVE methods are quite mature due to their close relationship to the linear finite element methods, while development of higher order finite volume methods remains a difficult and promising research front. Theoretical analysis, as well as the algorithms and applications of th...

Predicting the effective elastic properties of carbon nanotube-reinforced nanocomposites is of great interest to many structural designers and engineers for improving material and configuration design in recent years. In this paper, a finite element model of a CNT composite has been developed using the Representative volume element (RVE) to evaluate the effective material properties of nanocomp...

The occurrence of unphysical negative concentrations in solutions to diffusion equations is a well known and severe problem. Especially in three dimensions finite element discretizations give qualitatively very poor results, while finite volume discretizations are much more stable. We investigate the cause of these instabilities and trace them back to constraints on the mesh. It turns out that ...

A general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed. Basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated. Some numerical results are given to show the effectiveness and efficiency of the...