A natural mixed-element approach for the Stokes equations in the velocity-pressure formulation would approximate the velocity by continuous piecewise-polynomials and would approximate the pressure by discontinuous piecewise-polynomials of one degree lower. However, many such elements are unstable in 2D and 3D. This paper is devoted to proving that the mixed finite elements of this Pk-Pk−1 type ...

In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div) − Pk (1 ≤ k ≤ n) tensor spaces, enriched, for each n − 1 dimensional simplex, by (n+1)n 2 H(div) − Pn+1 bubble functions when 1 ≤ k ≤ n − 1, and by (n−1)n 2 H(di...

We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements...

Aspects of a method for 3D finite element computation of unsteady, incompressible freesurface flow are presented. The approach is based on the Deformable-Spatial-Domain/ Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the deformation of the elements in response to the motion of the free surface. The free-surface elevation is governed by a kinem...

Right ventricular (RV) dysfunction can serve as an indicator of heart and lung disease and can adversely affect the left ventricle. However, normal RV function must be characterized before abnormal states can be detected. We describe a method for reconstructing the 3D motion of the RV by fitting a deformable model to tag and contour data extracted from multiview tagged magnetic resonance images...

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviors of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational run...

This work introduces a new parallel wavelet-based algorithm for algebraic multigrid method PWAMG using a variation of the standard parallel implementation of discrete wavelet transforms. This new approach eliminates the grid coarsening process in traditional algebraic multigrid setup phase simplifying its implementation on distributed memory machines. The PWAMG method is used as a parallel blac...